Filmed in 3 days. Coincidentally, Apollo 11 took 3 days to reach the moon.
Michael Stipe described the song as being a "sad, funny tribute to a great man", actor/comedian/performance artist Andy Kaufman. Almost a decade later, R.E.M. would lend their music and title to Milos Forman's biopic Man on the Moon (1999), starring Jim Carrey.
Police shut down filming because the crew was on private property. When the cops recognized it was R.E.M., the shoot was allowed to continue.
Stipe sings until he enters into the bar at 3:19, where bar customers sing instead him but with his voice.