Operation Flashpoint and its sort-of-sequel Armed Assault does something along these lines. The AI has a field of view roughly corresponding to what most players have in a first person shooter (~90 degrees), and the AI can't see you if you're outside this field, but he can hear you if you do something noisy.

Time of day, weather (rain/fog), foliage, obstacles, stance, movement speed and inherent camouflage of the unit will affect visibility and 'audibility'. Each weapon has two properties describing how visible and how audible it is, so a .50 calibre rifle will light up as a Christmas-tree and a silenced pistol will be almost undetectable.

The AI shares information the same way players are forced to share information: by communicating it to its squad mates. When a bot spots an enemy, he will relay what he knows about that enemy with varying degrees of confidence and then start acting based on his standing orders. His group will react to this information in what's usually a logical way.

The specific situation you refer to, with the shot ringing out and the AI reacting to it, is one you will see quite often if you play these games. When you shoot any enemy AI in the area will start to learn things about you, the first of which is they know there's enemies about that are shooting, so they will hit the deck and run for cover. Pretty soon they will know your location and then two things generally happen: AI with machineguns, grenade launchers, sniper rifles and RPGs will seek cover near their current position and start firing towards you. Other AI will start moving to your last known position. If you stay put for too long, you will be overrun.

Now this of course sounds like the perfect AI, but there are naturally some issues. Sometimes the AI learns too much about you when you fire a weapon. The best example is C4 charges. Place some on a road, hide a ways off in some bushes, blow a truck up as the convoy passes. Now *all* the surviving AI in the convoy will have a fix on your location. Sometimes the AI doesn't learn enough of your position so instead of reacting logically to being fired upon (cover, suppressive fire, flank) they will just run around seeking cover, making it very easy to pick them off. There are some big path-finding issues when there's many obstacles around (such as in towns), particularly when the AI is operating a vehicle, so instead of chasing you down with their big-ass tank they will spend the better part of an hour trying to get through town.

When it works though, it's great.