Copper pans and mugs for Moscow Muels are classic and beautiful but require extra effort to keep them shiny and bright. Don't make the task any harder by putting them in the dishwasher. The harsh chemicals in dishwasher detergent will immediately dull the finish and can be corrosive and cause the copper to pit.
Pitting is not going to be removed even with the best copper cleaner and elbow grease.
Comment: Whew! I don't have copper so I don't have to worry about this one.