Are you aware that the Civ3 editor can be used to modify the rules of the game?
No city radius apearing on the main map. I find that a bit annoying, it makes placing cities a bit trickier without the grid on.
Turn the grid on. Turn it off when your done if you don't like how it looks.
Nowhere near enough fresh water sources especially on island maps. Even big islands rarely have a source of water. Not really a bug, just an annoying 'feature' of the map generator.
Open the editor, generate your random map, and add more fresh water. Generate ten maps at a time and pick a random map when you start up. The odds you'll remember all ten maps are slim. Maybe even find someone on the forums and create maps for each other, so you really don't know what they look like.
Barbarians are far too weak.
I think you can use the editor to determine what units barbarians can use but I may be wrong on that. Certainly having raging barbarians when you first start the game is a big pain in the ass IMHO.
Techs are too close together. Some units only have a few turns lifespan in the game.
Increase the stats on those units to make them more useful, thus prolonging their lifespan.
Inability to build obsolete units. Really annoying when you have Medieval Infantry and you want to build Gallic Swordsmen with their lovely 2 movement after your GA. 
The editor can be used to change the upgrade path if it bothers you that much. I can't think of another example other than Gallic Swordsmen off the top of my head where this applies.
You should be able to choose what cities get what resources without having a major fit trying to figure out road logistics. That way you can limit very low production/less vulnerable cities to producing older but still viable units without being too restricted as to what you can build.
There's a lot to the game already, and introducing a more complex resource system will have a major effect on game play. I don't see how "road logistics" are complicated. As long as you can draw a line from one point to another (it doesn't even need to be straight), you should be able to figure it out.
Espionage isnt a viable strategy.
Any idea what CIA's budget is? Exactly how many spies do you think they have? Espionage IS expensive. The game reflects this.
There's no recce units in the game which I was suprised about. After 1700 or so observation balloons should be units followed by spotter planes and UAV's to scout out enemy cities and troop movements for that turn. An upgrade path from Scout & Explorer would be obvious choices 
You could build your own unit...
