Monitors easily find themselves covered with greasy paw prints, including mine. Got lucky and found this discussion about monitor cleaning techniques.
Looked around the house and didn’t find any rubbing alcohol, a 50/50 solution (w/ distilled water) looks promising. I’ve not read all (there are a ton!) the discussion/comments but eventually plan to do so (this blog entry is a reminder! :-) Have a look, read and research, and post the findings somewhere (here?) I’ll do the same.