The mode dial on many Olympus C5060WZ cameras failed. Mine was one of them but I was lucky that I got a little more use then most with the same problem, even during the time it was failing~but because my problem occurred later there is not much info available anymore on getting it fixed.
Some owners suggest spraying WD-40 into the mode dial. You might also try contact cleaner with silicone. Here is a pdf showing how to replace dial - http://www.wrotniak.net/photo/c/_zip/c5060-dial-repair.pdf