Continuity mistake: The film starts in Muncie Indiana. There is a scene in the hills near the town. There are NO hills near Muncie, it's flat as a board.
Factual error: Parts of the scene where the brightly lit alien mothership passes directly over Devil's Tower are shot with the camera looking almost directly up, as would be the view from the people below. In these scenes, Devil's Tower remains totally dark despite having this huge light source directly above. The mothership is so huge that a shadow cannot explain this darkness.
Factual error: The aliens broadcast a series of pulses which are decoded by the scientists to be a longitude and latitude. In degrees:minutes:seconds, the longitude is 104:44:30 and the latitude is 40:36:10. These numbers are what the computer display shows and are what the scientists say (except for one slip-up in the hallway early in the scene where 104:40:30 is said). The scientists grab a globe and declare these coordinates are in Wyoming. Everybody and his brother (and the aliens) then proceed to show up at Devils Tower, Wyoming. However, Devils Tower is at around longitude 104 deg 44 min and latitude *44* deg 36min, not the *40* deg 36 min pulsed out by the aliens. If everyone had gone to 40 deg 36 min, they would have ended up in Colorado, more than a couple hundred miles south of Devils Tower, Wyoming.
Other mistake: In the climactic scene at the end of the movie when the alien mothership flies over Devil's Tower and the base, there is a shot of the mothership's shadow creeping along the ground, enveloping the shadows of the crew there. It's a dramatic shot, but since the mothership was not between the ground and the light source (the stadium lights of the base) it should not be blocking out the light, or creating a shadow.
Revealing mistake: The morning after Ronnie and Roy's big fight, Roy starts cleaning up his clay "sculpture." Before he pulls its upper portion off, you can see the pre-made seam (which is poorly disguised by the clay) where the top is attached to the bottom. When he tears it off, the lower portion is perfectly smooth and flat on top (simulating Devil's Tower) where it was obviously pre-cut.
Revealing mistake: In the scene where Ronnie cuts out a newspaper article about the UFO sightings, the night after Roy's first glimpse of the UFOs, two identical articles on Star Wars (1977) are on either side of the UFO article.
Continuity mistake: During the scene at the landing site the number of people on the landing pad varies dramatically from shot to shot.