Today I was having a closer look at the settings within ccsm (compiz manager) and managed to get a strange behaviour I experienced before. The screen was not refreshed if you move windows. Therefor it cluttered the complete screen, very ugly.
I started Ubuntu Tweak to restore my desktop settings, logged out and back in again but it did not fix the problem.
After looking closer to the problem I found that within Ubuntu Tweak there is a setting that will allow to hide the desktop icons. Once you enable it again the problem is fixed. For each icon set on the desktop it is possible to hide it.