I've been mining with my 7870@380Mhps, but I have to turn it off whenever I want to play games.
I plugged in my old 5750 so that I could mine at least a little bit while I was using the other card. But it can't mine.
With poclbm/guiminer it runs for a minute, then passes a verification error and quits.
With cgminer/bfgminer I get "[bf/c]gminer.exe has stopped working".
With Diablominer it runs fine at 120Mhps, but never accepts the blocks, and the number of "HW errors" slowly increases.

I would assume that the card is just borked, but it runs fine, tested with furmark for two hours with no errors, played a match of Dota 2 with it, ran 3dmark's benchmark.

EDIT:

Something even stranger: it runs at the expected speed with bitminter's client and returns no errors and confirmed blocks.