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.
Continuity mistake: The car the hybrid man pushes is in OK shape at first, then he lifts and flips it through the copper fence, and now its whole front side is gone. They might used an already wrecked "car double" for the scene when it crashes and explodes. (01:40:50)