The major weakness in Civ 3 are IMHO the Diplomatic and Combat AI routines. I think these need tweaking in Civ 4
1: A more robust and realistic Diplomancy Function with less random and irrational actions by the AI Civs, especially the latter.
An example would be a warning that an action you are about to undertake, or are doing, will lead to War, like building up massive Stacks just outside their borders, or attacking a third Civ even though they have no treatys with it.
I am not fond of having to constantly Ass Kiss the AI Civs with Gold and great Tech Gifts or deals so they don`t launch Kamikaze attacks against me, especially when we are more or less equal in Military and Research, IMO a bad design feature in Civ3 1.29.
2: A more realistic Combat system with Ancient units VS Modern units, right now you get too many groaners when that AI Spearmen kills 2 or more Veteran Tanks in a row.
The ability to "buy" or "rent" Mercenary units, a nice design featue that many other Civ type games offer.
The ability to "bribe" an AI unit in your terriority during War, this and the above offer the player interesting " decision points" in how to use his Gold.
In general a more expanded Tech Tree and PLEASE, less build time for the Key early city growth enhancements like Grainaries.
For the 10,000th. request, please stop the AI Civs from trying to build Cities on every available location, especially within your area of influence. AC seems to have gotten this right.
Last; please extend the Game End time out to at least 3000AD.