As insanely frustrating as this is, I'm relieved to know I'm not the only one experiencing this issue.
I have a 2009 MacBook Pro that I've had strange freezing issues with for some time now, but after I upgraded to Mountain Lion, I started experiencing the same things you all posted about. Screen flickering (from the bottom up), the screen would get all garbled-looking, pieces of windows would be left around the screen when dragging them around... and eventually it would all freeze (except for my cursor), and I'd be forced to restart from the power button. This happened probably about 3-4 times a day right after I upgraded to Mountain Lion.
I ended up taking my computer to the Apple store because of it. The first time, they replaced the logic board. I took it home, formatted my computer and did a fresh install of the OS it came with, and once again, upgraded to Mountain Lion. The next day, it started giving me the same issues as before. So I took it back to the Apple store a second time, where they replaced the entire display. Just got it back last night, and yet again, more screen flickering and freezing. đ
So in case anyone was worried that it might be a hardware-related issue, it looks like maybe we can rule that out (unless there's something left in my computer that they haven't replaced yet, that we all happened to have problems with at the same time... đ). Hopefully this is just some kind of a crazy bug in Mountain Lion that Apple has yet to work out.
Until then, if any of you happen to find a solution to this, please share!