Built a new PC for my bro-in-law's woman and she had this issue with grey lines on her 5770 XTX XXX Edition, running on an H55 chipset. I swapped hers with my own Gigabyte 5770 and seems to be ok so far for both of us (running mine on a P35-DQ6). Put it down to some weird combination of drivers/chips/brands.
On my combo (HD5870/3007WFP) I've only seen very rare glitches, once or twice a week maybe. Never had a crash or somehow abnormally colored screen (blue, black, grey, whatever) unless i used paint's fill tool on a full screen picture. ;D
In power management (BIOS) there's an option on my MB for HPET (High Precision Event Timer), enable that, then enable 64 bit mode (I have Win7 x64).
So my mobo is the Abit IP35 pro, and from what I can find searching online it doesn't have this option... If I was to install windows 7 32 (instead of 64 that I'm currently on) would that likely solve the issue? Not really wanting to buy a new mobo due to this. I never had this issue with my 8800gt... Believe it or not, this one issue has been frustrating enough that I wouldn't hesitate to go back to nvidia (next time). I've had all ati cards ever since the Radeon LE (except for the 8800gt).
The HPET can produce periodic interrupts at a much higher resolution than the RTC and is often used to synchronize multimedia streams, providing smooth playback and reducing the need to use other timestamp calculations such as an x86 CPU's RDTSC instruction.
Try dropping the clocks first, then dropping the voltage after the clocks have changed.