To start out, I really do love the game and all the new features and Firaxis really did a good job on getting all the different elements working well together. 
However, there were some bugs and a lot of annoyances or missing features that I think could really improve gameplay to make this one of the best games ever. So, here goes. Feel free to add more, I'll try and edit the list at least once a day. Some of these are already from other posts I've seen. I plan to send this to Firaxis in a few days, so they'll hopefully be implemented in a patch. Thanks.
Bugs
Can unload chariots from water onto Mountains
When you right click on a city, then open an advisor, the city menu stays there on top of everything and does not go away (becomes active again when you close advisor screen).
HP's are sometimes hidden when attacking.
The AI wants to expand so much that it mass produces settlers even if they have no where to go. (blocked in)
Workers set on auto will run far far far away to work on land when there's land that needs more improvement nearby. Also if you have 10, all 10 will go there, instead of separating to work on separate tasks. When they get there, 1 will start on the task and then the other 9 will turn around and go somewhere else.
The Iroquois start building the Sistine Chapel when we're in a major war and they only have 2 or 3 cities left (out of ~10). (Ok, so not a bug, just bad AI)
There is no indication that settlers are automated when you're trying to wake one from it.
Doesn't tell you when Wonders are obsolete.
The same "shuffle constantly between two tiles" bug I've seen in civ2 is back in civ3. In this case it was an automated worker, who for 6 turns entered and exited repeatedly one of my cities, as if they couldn't make up their mind.
After you lose a game, at the "dart board" screen when the other Civ's badmouth you, several time's I've had a black square at the very top where another Civ's head should have been (it talked, though there was no head there).
"Sort" function on the Domestic Advisor Screen is simply useless. As soon as you move the mouse, the order snaps back to the initial sort.
Cities in Civil Disorder are not marked in Domestic Advisor screen.
Workers set to auto-clean pollution (shift-p) will not go to a polluted tile which already has a worker on it (and some tiles take 8 turns for even an "industrious" worker to clean!)
Would not let you build the Forbidden Palace until you built a cathedral in the city.
Armies can't pillage
If you take over a city, governor doesn't take on the rules you've set for all your governors
Another Civ had no tech's to steal, yet it tried to allow the player to anyway, giving a blank screen with nothing to select.
Control-Shift-G gives you a go to town list. However, you can't leave without selecting a city.
When you draft people, it doesn't show anything happen until you press something else in the city (like change production). This may cause unwanted multiple drafts.
Features/Annoyance Fixes
Seeing what enemies are going while waiting (color)
An option to draw borders on TOP of all terrain. It's impossible to find them in the large jungle/forests.
Have the info window show unit hp, other units in the square and (if it's a worker) show what improvements are already there
When city is in disorder, pop up and option to zoom to it.
Add Diplomacy option: Demand tribute.
When fortified, make a lot easier to see (a F would be nice).
Ability to Sentry and Patrol units.
When you meet a new civ's unit or sphere of influence (preferably unit), have it automatically bring up a diplomatic session with them.
Have a sound effect for Orders/Moves you can't do when you try them (e.g. irrigate when you can't)
Let you establish embassies from the Diplomacy screen
Let you view the city screen while determining whether you want to Capture or Raze a city, after you capture it.
No mass wake/activate/fortify/upgrade options from right-click menu's (as opposed to shift-commands)
Show how much movement units have left (fractions with roads)
The tax bar likes to bounce back when trying to move it just 10 percent either way.
Have a button you can press so all your automated/units on Go commands go (that you can press at beginning of turn, if you wish).
Notify you when you produce a unit that you can upgrade to.
Label the hurry/draft buttons or have pop up labels.
Right-click civilopedia info from city screen when changing build options.
List built units/improvements/wonders that happened on current turn.
Make starting positions an option.
Need a way to see how many shields you have built out of how many needed from city advisor screen.
Need a way to show how a Civilization's Ability in effect. (i.e. Somehow show extra shields being produced for Industrious civ's)
Draw City Radii on main map (at least an option).
Zoom Function in the map editor.
Pick tech's given from "Theory of Evolution"
In Diplomacy, let you ask another to make peace with another Civ (so you won't be drawn into a war from mutual protection pact)
Create a "Find Resource" option
Add option in diplomacy to ask for another Civ to Vote for you
Option to list all ongoing trades with other Civilizations
Would be nice if the advisors were more specific. They say "Spend more on science" when you are already at 100% Science.
Add a Build Vector where you can automatically send troops to another city when they're built
Stack movement.
Ability to see the destination of units on Go To.
Repeat Build feature in City Queue.
Ability to sink ships with bombardment.
Ships should "wake up" when units are loaded into them. (Both from the existing fortify command, and the already-requested sentry command.)
Enable access to Civilopedia during negotiations (similar to SMAC's "Pardon me while I consult the Datalinks.")
The tiny little white bars displayed in squares with multiple units are often hard to see. Possible alternatives:
a. Display an easier-to-see number indicating the number of units in the square, or
b. Bring back CIV2's display of "n other units" somewhere on the bottom of the screen.
Ability to see World Map / Resource Info / Other pertinent info during Diplomacy Negotiations.
Ability to turn off Worker animations.
Additional option on Automated Worker Popup screen: Ideally, the screen that pops up when you click on an automated worker should have an additional option, like this:
1. Stop current task
2. No, carry on
3. Finish current task, then wait for new orders
If you have an embassy with another civilization, you should get messages, ala Civ2, when they advance in technology, trade in technology, and especially when they take over a city from another civilization.
Right clicking on an empty tile gives you info about the terrain. A second right click anywhere on the map to get rid of the popup window would be really nice.
Enable the Page Up/Page Down keys for the scrolled lists in the Advisor screens.
Add display of strategic resources to the mini-map. Perhaps a third view, in addition to the terrain and territory view, could be added. (This would be tough to implement well, however, as letters may be too big, and colored dots would be hard to distinguish)
Add an automated worker option (keyboard shortcut would do) to put a worker on a permanent Plant Forest/Chop Down Forest cycle:
If the square is not the correct type to plant forest, ignore. Otherwise:
1. If there's no forest in the current square, plant one.
2. If there is a forest, chop it down.
3. Repeat.
Possible Bugs
It seems that enemy capitals decrease waste and corruption in your own city's if your citys is close to said enemy capital.
Air Superiority (and Coastal Fortress) seems to be completely broken for the human player. (never seen one of the fighters take down a bomber)
Smart Weapons are broken for humans.
Lose big armies when city is culturally assimilated
Fortress doesn't give ZOC
Rifleman making firing sounds when moving.
Space Race movie doesn't play on minimum install
The AI seems to move his offensive units around all the time even if he has no where to go. I saw a 3 square island with a city in the middle and the AI would send armies back and forth to the squares for no apparent reason.
Sometimes, you can't update units even if they are in a city with a barracks. Not sure why.
In some games, Palace Upgrades never take place.
Inability to airlift after airlift: City A has airport and airlifts unit to City B. Next turn, City A cannot airlift anymore. Turn #3 Still can't airlift. Turn #4, ability to airlift is regranted.
If you have a unit who is fortified in a city and build another unit, then activate the first unit and fortify the second unit while in the city view via right-clicking the game will lock up. (Seen w/o just building a unit, but moving a unit in the city as well)
You can only airlift 1 unit per turn out of a city with airport, but you can lift as many as you want in.
The computer can irrigate from ocean squares (no rivers, pre-electicity). This may be as intended though?
Subs are not hidden from computer. ie. they are recognized as being on an ai's territory. "After building my first subs last night and popping them inside some Zulu territory, I very quickly got the 'move your forces' dialogue from Shaka."
Moving a carrier toward a land square brings up a menu to unload your bombers. If you choose to unload them, the game crashes.
Edit-
11/3 - Added 4 items
11/4 - Added 13 items
11/5 - Added 9 items
11/6 - Added 9 items
11/9 - Added 7 items
11/10-Added 7 items
11/11-Added 1 item
11/14-Added 8 items
However, there were some bugs and a lot of annoyances or missing features that I think could really improve gameplay to make this one of the best games ever. So, here goes. Feel free to add more, I'll try and edit the list at least once a day. Some of these are already from other posts I've seen. I plan to send this to Firaxis in a few days, so they'll hopefully be implemented in a patch. Thanks.
Bugs
Can unload chariots from water onto Mountains
When you right click on a city, then open an advisor, the city menu stays there on top of everything and does not go away (becomes active again when you close advisor screen).
HP's are sometimes hidden when attacking.
The AI wants to expand so much that it mass produces settlers even if they have no where to go. (blocked in)
Workers set on auto will run far far far away to work on land when there's land that needs more improvement nearby. Also if you have 10, all 10 will go there, instead of separating to work on separate tasks. When they get there, 1 will start on the task and then the other 9 will turn around and go somewhere else.
The Iroquois start building the Sistine Chapel when we're in a major war and they only have 2 or 3 cities left (out of ~10). (Ok, so not a bug, just bad AI)
There is no indication that settlers are automated when you're trying to wake one from it.
Doesn't tell you when Wonders are obsolete.
The same "shuffle constantly between two tiles" bug I've seen in civ2 is back in civ3. In this case it was an automated worker, who for 6 turns entered and exited repeatedly one of my cities, as if they couldn't make up their mind.
After you lose a game, at the "dart board" screen when the other Civ's badmouth you, several time's I've had a black square at the very top where another Civ's head should have been (it talked, though there was no head there).
"Sort" function on the Domestic Advisor Screen is simply useless. As soon as you move the mouse, the order snaps back to the initial sort.
Cities in Civil Disorder are not marked in Domestic Advisor screen.
Workers set to auto-clean pollution (shift-p) will not go to a polluted tile which already has a worker on it (and some tiles take 8 turns for even an "industrious" worker to clean!)
Would not let you build the Forbidden Palace until you built a cathedral in the city.
Armies can't pillage
If you take over a city, governor doesn't take on the rules you've set for all your governors
Another Civ had no tech's to steal, yet it tried to allow the player to anyway, giving a blank screen with nothing to select.
Control-Shift-G gives you a go to town list. However, you can't leave without selecting a city.
When you draft people, it doesn't show anything happen until you press something else in the city (like change production). This may cause unwanted multiple drafts.
Features/Annoyance Fixes
Seeing what enemies are going while waiting (color)
An option to draw borders on TOP of all terrain. It's impossible to find them in the large jungle/forests.
Have the info window show unit hp, other units in the square and (if it's a worker) show what improvements are already there
When city is in disorder, pop up and option to zoom to it.
Add Diplomacy option: Demand tribute.
When fortified, make a lot easier to see (a F would be nice).
Ability to Sentry and Patrol units.
When you meet a new civ's unit or sphere of influence (preferably unit), have it automatically bring up a diplomatic session with them.
Have a sound effect for Orders/Moves you can't do when you try them (e.g. irrigate when you can't)
Let you establish embassies from the Diplomacy screen
Let you view the city screen while determining whether you want to Capture or Raze a city, after you capture it.
No mass wake/activate/fortify/upgrade options from right-click menu's (as opposed to shift-commands)
Show how much movement units have left (fractions with roads)
The tax bar likes to bounce back when trying to move it just 10 percent either way.
Have a button you can press so all your automated/units on Go commands go (that you can press at beginning of turn, if you wish).
Notify you when you produce a unit that you can upgrade to.
Label the hurry/draft buttons or have pop up labels.
Right-click civilopedia info from city screen when changing build options.
List built units/improvements/wonders that happened on current turn.
Make starting positions an option.
Need a way to see how many shields you have built out of how many needed from city advisor screen.
Need a way to show how a Civilization's Ability in effect. (i.e. Somehow show extra shields being produced for Industrious civ's)
Draw City Radii on main map (at least an option).
Zoom Function in the map editor.
Pick tech's given from "Theory of Evolution"
In Diplomacy, let you ask another to make peace with another Civ (so you won't be drawn into a war from mutual protection pact)
Create a "Find Resource" option
Add option in diplomacy to ask for another Civ to Vote for you
Option to list all ongoing trades with other Civilizations
Would be nice if the advisors were more specific. They say "Spend more on science" when you are already at 100% Science.
Add a Build Vector where you can automatically send troops to another city when they're built
Stack movement.
Ability to see the destination of units on Go To.
Repeat Build feature in City Queue.
Ability to sink ships with bombardment.
Ships should "wake up" when units are loaded into them. (Both from the existing fortify command, and the already-requested sentry command.)
Enable access to Civilopedia during negotiations (similar to SMAC's "Pardon me while I consult the Datalinks.")
The tiny little white bars displayed in squares with multiple units are often hard to see. Possible alternatives:
a. Display an easier-to-see number indicating the number of units in the square, or
b. Bring back CIV2's display of "n other units" somewhere on the bottom of the screen.
Ability to see World Map / Resource Info / Other pertinent info during Diplomacy Negotiations.
Ability to turn off Worker animations.
Additional option on Automated Worker Popup screen: Ideally, the screen that pops up when you click on an automated worker should have an additional option, like this:
1. Stop current task
2. No, carry on
3. Finish current task, then wait for new orders
If you have an embassy with another civilization, you should get messages, ala Civ2, when they advance in technology, trade in technology, and especially when they take over a city from another civilization.
Right clicking on an empty tile gives you info about the terrain. A second right click anywhere on the map to get rid of the popup window would be really nice.
Enable the Page Up/Page Down keys for the scrolled lists in the Advisor screens.
Add display of strategic resources to the mini-map. Perhaps a third view, in addition to the terrain and territory view, could be added. (This would be tough to implement well, however, as letters may be too big, and colored dots would be hard to distinguish)
Add an automated worker option (keyboard shortcut would do) to put a worker on a permanent Plant Forest/Chop Down Forest cycle:
If the square is not the correct type to plant forest, ignore. Otherwise:
1. If there's no forest in the current square, plant one.
2. If there is a forest, chop it down.
3. Repeat.
Possible Bugs
It seems that enemy capitals decrease waste and corruption in your own city's if your citys is close to said enemy capital.
Air Superiority (and Coastal Fortress) seems to be completely broken for the human player. (never seen one of the fighters take down a bomber)
Smart Weapons are broken for humans.
Lose big armies when city is culturally assimilated
Fortress doesn't give ZOC
Rifleman making firing sounds when moving.
Space Race movie doesn't play on minimum install
The AI seems to move his offensive units around all the time even if he has no where to go. I saw a 3 square island with a city in the middle and the AI would send armies back and forth to the squares for no apparent reason.
Sometimes, you can't update units even if they are in a city with a barracks. Not sure why.
In some games, Palace Upgrades never take place.
Inability to airlift after airlift: City A has airport and airlifts unit to City B. Next turn, City A cannot airlift anymore. Turn #3 Still can't airlift. Turn #4, ability to airlift is regranted.
If you have a unit who is fortified in a city and build another unit, then activate the first unit and fortify the second unit while in the city view via right-clicking the game will lock up. (Seen w/o just building a unit, but moving a unit in the city as well)
You can only airlift 1 unit per turn out of a city with airport, but you can lift as many as you want in.
The computer can irrigate from ocean squares (no rivers, pre-electicity). This may be as intended though?
Subs are not hidden from computer. ie. they are recognized as being on an ai's territory. "After building my first subs last night and popping them inside some Zulu territory, I very quickly got the 'move your forces' dialogue from Shaka."
Moving a carrier toward a land square brings up a menu to unload your bombers. If you choose to unload them, the game crashes.
Edit-
11/3 - Added 4 items
11/4 - Added 13 items
11/5 - Added 9 items
11/6 - Added 9 items
11/9 - Added 7 items
11/10-Added 7 items
11/11-Added 1 item
11/14-Added 8 items
