Geforce 7050 renders black and sometimes crashes Unity

This issue was originally filed in Launchpad in these two bugs:

I was asked to report this issue here, since it only seems to happen on this piece of hardware.

In the latter bug, Compiz crashes quite often when you have more than 4 windows open and are running Unity. This issue has existed since at least Precise. This is suspected to be caused by undocumented driver behaviour.

The first bug only happens in the very newest Raring release running Unity. Windows are rendered as black squares. When you force updates on specific parts of the window, they are rendered properly. The rest of the window remains black. A video demonstrating this can be downloaded here.