First off, I hope no one at Firaxis or Take Two is troubled by this thread. I love this game, and the manual is great. But no one is perfect, especially when writing a 200 page manual under deadline pressure.
So I'd like to share what I've learned - it took me a while to confirm that the manual was in fact wrong in a few places and I'd like to get a thread going with corrections here. It might save a little time for people just learning the game, and I'm sure I'll learn something too.
I'll try to add everyone's additions to the list, and hopefully the moderators will sticky this thread.
Corrections
Combat Odds: Ignoring first strikes, if one unit has double the strength of the other in combat, it has around a 99% chance of winning. (The manual incorrectly says 2-1 on page 40.)
Barracks: Units start with 4 experience points if built in a city with a barracks, not 2. (page 45)
Industrious Trait: The industrious trait increases wonder building by 50%. The manual states 50% in some places and 100% in others (page 96).
Great Engineers: Great engineers can't hurry the construction of spaceship parts. They also can't hurry The Internet. (page 96)
Renaming Cities: You can rename cities by clicking on the name of the city in the "examine city" screen. (The manual says city names cannot be changed on page 45.)
Resources and construction speed: Having the appropriate resource for a wonder doubles construction speed, rather than halving it as the manual says on pages 112-122. With the resource, ten hammers become twenty; this also applies to hammers from cutting down forests.
Omissions
Aggressive Trait: Units that get the combat 1 promotion from the aggressive trait still get additional promotions when they reach 2 experience points, then 5, 10, and so on. (page 159)
Unresolved
Fighters: In Ch 3 (p 130), it says that the intercept chance is 40% and bombard is -15%. In the Appendix (p 200), it says the intercept is 50% and bombard is -5%.
Jet Fighters: In Ch 3 (p 131), intercept is 60%. In the Appendix (p 202), the interccept is 70%.
And from the readme, for easy reference:
MANUAL ERRATA AND ADDENDUM
Hotkey / Interface Changes
* [ESC] will close every screen.
* Pillage hotkey was changed to [Shift – P]
* Improve Nearest City (Automated) is now [Shift - Ctrl - C]
* Intercept hotkey was changed to
* Contact Civ Pop-up by pressing [Shift – D]
* To a activate Voice over IP in multiplayer, press the [Scroll Lock] key.
* You can declare war by pressing [Alt] and clicking on the name of the enemy leader in the score display.
* To change a units name just click on their name on the bottom left side of the screen.
Gameplay Changes
* Spy does not cost any gold per turn
* Calendar now centers the world map (instead of Astronomy)
* Border expansion occurs in a city when the city’s culture is 10, 100, 500, 5000, 50000 (Normal Game Speed)
So I'd like to share what I've learned - it took me a while to confirm that the manual was in fact wrong in a few places and I'd like to get a thread going with corrections here. It might save a little time for people just learning the game, and I'm sure I'll learn something too.
I'll try to add everyone's additions to the list, and hopefully the moderators will sticky this thread.

Corrections
Combat Odds: Ignoring first strikes, if one unit has double the strength of the other in combat, it has around a 99% chance of winning. (The manual incorrectly says 2-1 on page 40.)
Barracks: Units start with 4 experience points if built in a city with a barracks, not 2. (page 45)
Industrious Trait: The industrious trait increases wonder building by 50%. The manual states 50% in some places and 100% in others (page 96).
Great Engineers: Great engineers can't hurry the construction of spaceship parts. They also can't hurry The Internet. (page 96)
Renaming Cities: You can rename cities by clicking on the name of the city in the "examine city" screen. (The manual says city names cannot be changed on page 45.)
Resources and construction speed: Having the appropriate resource for a wonder doubles construction speed, rather than halving it as the manual says on pages 112-122. With the resource, ten hammers become twenty; this also applies to hammers from cutting down forests.
Omissions
Aggressive Trait: Units that get the combat 1 promotion from the aggressive trait still get additional promotions when they reach 2 experience points, then 5, 10, and so on. (page 159)
Unresolved
Fighters: In Ch 3 (p 130), it says that the intercept chance is 40% and bombard is -15%. In the Appendix (p 200), it says the intercept is 50% and bombard is -5%.
Jet Fighters: In Ch 3 (p 131), intercept is 60%. In the Appendix (p 202), the interccept is 70%.
And from the readme, for easy reference:
MANUAL ERRATA AND ADDENDUM
Hotkey / Interface Changes
* [ESC] will close every screen.
* Pillage hotkey was changed to [Shift – P]
* Improve Nearest City (Automated) is now [Shift - Ctrl - C]
* Intercept hotkey was changed to
* Contact Civ Pop-up by pressing [Shift – D]
* To a activate Voice over IP in multiplayer, press the [Scroll Lock] key.
* You can declare war by pressing [Alt] and clicking on the name of the enemy leader in the score display.
* To change a units name just click on their name on the bottom left side of the screen.
Gameplay Changes
* Spy does not cost any gold per turn
* Calendar now centers the world map (instead of Astronomy)
* Border expansion occurs in a city when the city’s culture is 10, 100, 500, 5000, 50000 (Normal Game Speed)