Uninstall your current drivers. Roll back to the 12.1 officials or 12.2
preview, whichever works best on your system. (12.2 previews are safe and artifact free. 12.2 officials and pre-certifieds are not.)
If you have a 64-bit OS, you can get the 12.1s http://support.amd.com/us/gpudownload/windows/previous/Pages/radeonaiw_vista64.aspx, if you have 32-bit you can get them http://support.amd.com/us/gpudownload/windows/previous/Pages/radeonaiw_vista32.aspx. Download the driver package you want, then uninstall your current drivers. (This can be done via the Change/Remove control panel in Windows--just look for the AMD Catalyst Install Manager.) Reboot, reinstall with your chosen driver package, reboot again. Profit.
This is a well-known issue with the 12.2s, and as such they should be avoided at all costs if you're intending to play Skyrim with a pre-7xxx series card. AMD claims they'll be fixed when the 12.3s come out, presumably sometime at the end of this month. Until then, stick with whatever older driver works best for you, and avoid 12.2 like the plague.