AI War is actually frame-locked to something like 20fps, but it depends on what performance profile you select. So if you lock it to 60fps, you'll get all sort of oddities. The reason the framerates are so limited with AI War is the extreme cost of calculating each frame (in terms of units moving around and so forth). Rendering the same frame 3 times if nothing has changed also just doesn't make any sense, so there's no point having frames that don't match up with the changes in actual unit positions and so forth.
That said, if you want to run the game at 60fps, the top performance profile in there lets you do that. But it will absolutely come to a standstill on large battles, even if you're on a really powerful machine.
In terms of graphical artifacts and tearing and so forth, this is because the ATI drivers are, well, terrible. There's documentation about this all over the Internet, and it affects all sorts of games in different ways. Generally the solution is to go back to an older set of drivers before they got all glitchy. I can't remember the version numbers that are considered safe, but some folks have posted them elsewhere in these forums. I may be way off, but I think it started with a 9. I really hope that the drivers for ATI get sorted out, but in the meantime they're causing all manor of havoc.
