Mindless Diplomatic AI
In which the AI declares wars and ends them without rhyme or reason. Small countries entirely surrounded by gigantic empires suicidally invade and fight to the death. Allies surrounded by enemies declare war on each other. etc
Player Hating Diplomatic AI
In which the AI will launch a blood vendetta against the player for no good reason but to make the game harder, even to the detriment of realistic diplomacy of the time. Trying to fight off the Moors in Spain during the Reconquista? Good luck with that, because the French, English, Germans, and Italians are all going to be stabbing you in the back for no reason, while anyone you ally with will instantly attack once you gain a land border regardless of strength, common enemies, etc
Boring Victory Conditions
In which you reach a point where you have won, but you haven't really "won" until you hunt down and kill that last enemy scout wandering the map.
Broken Naval AI
In which the AI is either incapable of using boats and sits around on its island waiting to be put down (eg. Age of Empires 2), or in which the AI completely cheats with its naval abilities, leading to such scenarios as Japan sending naval forces to conquer the Baltics during WW2.