I can't imagine that this is the very first post on the inconsistencies of pathfinding near cities, but I haven't seen any talk about it recently, or, IIRC, at all from the developers. Basically, if you have resources or stamps near a city, your city will adopt some wierd shapes. I don't really want to break out the graphics, but imagine if your city is a square in each direction away from a river, a lumber mill, and it's kitty corner to an iron mine. It will not be rectangle-shaped.
Any such shape seems to confuse the hell out of the AI. Sometimes, if you are sending a unit that is on a tile next to a city to another tile next to that city, the unit will move there without having used any of its movement points. Other times, it will decide to foot it around the city, which, lest we forget, is about 6 months of game time. THIS MATTERS: If i have some units I want to keep in a city, while a reinforcing army takes care of a threatening enemy one, I want to attack that army THIS TURN. Or, at the very least, to know that I can't attack that army this turn before I send my unit on a 3-turn trip through a nearby forest.
Finally, there appears to be some kind of cap on how many units can be in a city tile. Some armies just *wont* go into a city if there are already units there. Is this a bug, and if not, what is the cap and how are the players supposed to be informed of it?