Re: Graphics Artifacts 6800 Ultra AGP :(
If possible, try the card in another computer and see if it does the same thing.
I had very similar problems with my 6800 (non ultra) and pushing alt + tab did fix it temporarily, but same as you they appeared shortly after. I tried it in another computer and it ran fine, no tearing at all, so after a bit of trial and error I came to the conclusion that my AGP port on my mobo had gone.
Test it in another rig first and if it still happens well at least you know it is actually the card, as in my case it wasn't.