Training is always a good idea. It might help in the long run, but in the short term you might have to limit his access to such wonderful things ( like really good smelling food ). What might be the most challanging for you is how Roscoe is getting rewarded for his bad behavior, getting in the trash is food reward, getting in the crock pot another food reward, licking dishes yet again rewarding himself. Think about maybe making it harder for Roscoe to get into the trash maybe a can with a lid, also maybe rinse the dishes so he won't have any reason to help himself. If he is not getting self rewarded he might give up on the bad behavior. Also like has been suggested make sure he has lots of other things to do. Does he have a Kong?? How old is your dog?
Sorry about all the questions I just want to give you the best advice I can.
Good luck.
Gina