I am posting this again because I have changed to VMWare Player and I discovered something new.

I am running Ubuntu 12.04 LTS (Guest) in VMWare Player 6.0.2 on Windows 7 64-bit Host. I have VMWare Tools installed properly.
I am running MATE but the problem persists when I change (to and from) xfce, gnome, mate a-- and back again I had been using this for a couple of years without any graphics issues. After an Ubuntu update (typical) -- my video is corrupt and will not refresh correctly.

My desktop icons are "mirrored" and when I open a terminal window (for instance) -- sometimes -- the window appears multiple times.
Of course, only one is the real image. It seems to be a refresh problem.
When I move an active window around the screen the "older" images "erase" and my icons (for instance) are in the correct location.
For instance, I can move the terminal around a pretty corrupted window and the screen behind it is repainted correctly.

NEW:

Next, I got the idea to try and Remote Desktop in to the Ubuntu 12.04 LTS Guest OS from my Windows 7 64-bit Host.

Once working, and connected via Win RDC -- using MATE as default in my /etc/xrdp/startws.sh -- my video is not corrupted and works fine (as in the past).

Any ideas about what is going on ? or how to fix this ?