Probably no fix at all: read all this topic and you'll there's a bug, related to graphics, with all kernels based in the current patch set (BronzovkAnVoodooSinetek) when running in 64-bit kernel mode (which is the only option for Mountain Lion. So your card is one of the unlucky ones. If it was, say, a 6xxx card, i'd say just use Lion, since you can boot in 32-bit kernel mode in 10.7.x. But your card needs 10.8.3 and above, so you'll have to wait for a fix in the kernel. Sorry, dude!
If you can live without QE/CI, just remove AMDRadeonAccelerator.kext from the system.
All the best!
P.S.: out of curiosity, the artifacts are everywhere or only with browsers (Safari, Firefox etc)? If it's only with browsers, just open the Preferences menu of the browser and disable hardware acceleration/composite drawing/canvas composition (it's different for each one)