Windows appear behind the panel

I had the same problem in Ubuntu 12.04 with GNOME. Indeed it could be fixed with compiz: enable "Place Windows" in Category/Windows Management.

I had this too on a machine that was all the way upgraded from Intrepid and the problem did not appear for a dummy new user I created for investigation purposes. This is how I solved it:

I logged out of unity, switched to a virtual terminal hitting AltF1, logged in as root, killed all remaining processes from my usual login with killall -u <login>, did a cd /home/<login> and a mv .gconf .gconf-old. When logging back in, the issue had disappeared with a lot of others for the price of losing some configurations which I considered a bargain.

After some diffing .gconf with .gconf-old with meld, I reached at the conclusion that some pre-natty compiz settings were the most probable cause, but your mileage may vary.