I think this is also what I am experiencing... For me the problem is that the graphics driver claims to support OpenGL and GLX but lacks important features for Unity. Due to some changes in Unity it won't fall back to slow mode automatically. Try to add the following file:
# /etc/X11/Xsession.d/99try_slow_mode
export LIBGL_ALWAYS_SOFTWARE=1
Then reboot and see if it works. This essentially forces all applications to fall back to software 3D rasterizer which is slow. I think they are currently trying to add some smarter fallback and I'd like to see that it gets fixed.
It also looks like there is currently nothing one could do to disable some effects in Unity so it will work with implementations of older graphics drivers.
To revert back simply delete the file and reboot.
Amendment: Just in case someone wants to collect this, my GPU is AMD Mobility Radeon 7500 [RV200]...