The Ai falls for the same ploy all the time on the battlefied. I hide a few units of fast, skirmishing cav (Jinettes, Turkoman etc...) and when the enemy army passes I have them fire at their general. The general's unit invariably chases the annoying cav away and promptly gets cut off from it's army and crushed by my heavy cav.
Of course this doesn't happen nearly as often as I'd like, but the fact that it happens at all shows the AI doesn't understand the basics of tactics. I've never yet seen the AI use a feint or a false withdrawal like I do, and they fall for them every time I use them too.

Also agree that the most annoying aspect is the refusal to make peace when they are nearly wiped out. I don't like destroying a faction completely (maybe I play Civ 3 too much), but I have no choice. In fact the only time I've ever seen the enemy faction makes peace is when it had a strong position and could afford to fight on. I think of it as the bitterness of a defeated foe refusing to give in. They wish to die to the last man and usually do.

Actually, thinking again, it makes more sense for the AI to refuse to make peace when they have only one cruddy province left. An AI faction could never recover and become a major player from Cyrenecia, but if it was destroyed then it could well return years later with half-a-dozen large armies. I once saw the Turks destroyed twice in one game only to reappear stronger each time. They even managed to take Constantinople the third time round (until I relieved it from their hands with my longbows and billmen).