Not sure what to call this problem... or what to search on...
I've equipped myself, my wife, and my dad with PowerBook 12's.
Have only seen this problem with my dad's PB12 (rev C, I believe)...
We'd seen it a few times when waking it up from sleep; and today after a system update, we restarted and got a new flavor of the problem...
The after-sleep problem: the display on the screen looks like you took random rectangles of what's supposed to be displayed and replicated them in random places on the screen. If a dialog pops up, you might see it fairly intact in two places, but then a corner of it in a couple other places. If you try to pull down the system menu, an appropriate area "pulls down", but its alternating strips of the desktop and the menu in such a way that you can't read the menu at all. If you pull up the dock from the bottom, it shows up somewhat munged underneath the menu bar.
The after-restart problem: each window displayed would display its appropriate rectangle, but the entire inside of the rectangle would be some portion of the desktop image. Kind of like the windows were "cloaking" or doing the "Predator" thing... you can sorta see their outline, but otherwise it looks like nothing is there but a shifted desktop pattern.
Re-starting the computer seems to clear up the problem.
Any ideas? Bad video card?