Continuity mistake: During the climax, when the old-fashioned Atari-controller is lowered down from the UFO, watch closely. In the first two shots, it's swinging back and forth rather quickly and dramatically, however, immediately from the third shot on, it's suddenly barely swinging. It's too instantaneous between edits to be the result of it naturally losing momentum.
Revealing mistake: About seven minutes in, during the scene where we see Cooper helping the Nerd as a cameraman, you can tell that Cooper has been added to the scene using green-screen effects, as the actor was unavailable to shoot at the location. The lighting on Cooper doesn't quite match the lighting of the scene, and you can see a slight "blur/feathering effect" around him where the greenscreen background was removed.