make sure you run 'fglrxconfig' in the console after you install it to set it up.
Then go download Enemy Territory (
www.castlewolfenstein.com)! Best free First Person shooter game ever!
Then make sure you set the game to run on your desktop resolution. My desktop resolution is 1024x768 but I was running the game in 800x600 and got all these graphical tearing and glitches. But once you set the game up in 1024x768, the tearing and graphical glitches go away.