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.
Continuity mistake: When Jane is in the night school, the position of knife and fork on the plate changes between shots. Both on one side (close up) or one on each side (long shot).
Continuity mistake: When April shoots the alien, they all go outside to look at it. Behind them, you can see the windows boarded up, but they don't board them up until later in the movie.