I seem to remember that the Police cars in <i>Grand Theft Auto</i> were notrious for ramming the back of my vehicle repeatly and blowing themselves up as a result, while at the same time, failing to notice an army tank holding a mutiple felon that has just wrecked half the city because you presumably painted it a different color and put a different set of plates on.
Many shooters have problems with the fact that you can fire off machine guns and rocket launchers, but unless someone sets off an alarm, there are enemy troops that will be caught unawares regardless (Ummm, the machine gun fire doesn’t make you wonder if something’s wrong?)
<i> Theif</i> had a part where you need to break into a prison to rescue someone. At one point, you hear a guard whistling constantly, not far from other guards. If you knock him out, I wondered about the fact that the other guards didn’t seem to notice the whistling had stopped. Same with guards walking a patrol route. Wouldn’t someone notice when they guard failed to pass by after so many minutes(particulary if they normally passed another guard.
Maybe not so much poor AI for most of these, but rather, really stupid guards and enemies.