Update2: I found a much more general solution to the redraw problem.
Update: I'm not sure if that worked or not. I think it improved the situation, but didn't fix the refresh problems entirely.
I've been using Sketchup successfully for quite a while now in Ubuntu linux. The trick was to install the wine PPA in order to get a more recent version of wine than Ubuntu distributes by default.
However, at home I had screen update problems: for instance, when I'd mouse over a face with the push/pull tool, it wouldn't draw in the crosshatching until I left the face.
But today I figured out how to solve the refresh problems, thanks to a comment in the wine appdb entry for sketchup 7. I ran nvidia-settings, then set:
NVIDIA X Server Settings manager checked
Antialiasing Settings - Override Application - Off
Anisotropic Filtering - Override Application - 1x
The next time I started up sketchup, it worked fine.