Did any dinosaur molt?
Richard Prum (the author of Evolution of feathers) says that ornithology is mostly a science about dinosaurs. He insists that dinosaurs were very close to birds, part of them had feathers and these feathered dinosaurs "shed (molt) them as birds of our days do".

Thus, we can conclude that dinosaurs probably possessed at least one molting-like mechanism, while others are the subjects for consecutive investigations. 

sources
Moulting tail feathers in a juvenile oviraptorisaur. Nature, 2010.