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.
Character mistake: When Ronnie is cutting the article about Roy's encounter out of the newspaper, the title of the article begins with "UFO's...", the apostrophe making it possessive. It correctly should have been "UFOs...", with no apostrophe making it plural as intended.
Plot hole: The aliens provide coordinates for a place to make a rendezvous with humans but do not specify a time. It's possible they're monitoring and will arrive when they see enough humans gathering at Devil's Tower, but the humans seem to expect the aliens to come more or less exactly when they actually do, somehow.
Continuity mistake: When Roy first encounters the alien ship at the railroad crossing, when the bright light comes on, he leans out of the truck window, and the right side of his face is exposed to the light. Therefore, it is the right side of his face that should have been burned. Subsequent shots show that the left side of his face is burned. (00:21:00)