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.
Character mistake: "Cosmic Kidnapping" is spelled incorrectly with a missing P in a newspaper article at the press conference where he breaks his pencil while drawing.
Factual error: When Barry first appears in the middle of the road, you can see the constellation Orion in the upper right of the scene. From mid-northern latitudes, Orion is visible in the evening from October to early January and in the morning from late July to November. The scene looks like a summer evening and if it was the morning Orion would not be that high in the sky.
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.
Factual error: When Roy discovers that he has built a model of Devil's Tower as a result of an ABC news broadcast by Howard K. Smith, the remote reporter on site refers back to the anchor as "Walter" (Cronkite, as proved during Roy's interrogation), who worked for CBS, not ABC. (CBS did not allow Spielberg to cast Cronkite, and the dialogue was not redone to account for Smith).
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.
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.
Factual error: Roy has the TV on during the creation of the Devil's Tower model. The show Days of Our Lives is on. When it cuts away, a Budweiser commercial comes on. Beer commercials are never on during daytime weekday soap operas. Then the news comes on and it's ABC news. Days of Our Lives is on NBC and always has been.
Continuity mistake: In the alien departure scene at the very end of the film, a solitary alien exits the mothership and approaches Francois Truffaut, who extends his right hand directly towards the alien and makes the Five Tones hand gesture. The camera cuts to another angle half-way through the gesture, and we see that Truffaut is now looking sharply to his right, over his extended arm, and smiling broadly at the alien as he completes the hand gesture. Apparently, Truffaut's body and extended arm pivoted 90° away from the alien mid-way through the 2-second gesture.
Revealing mistake: When the gigantic mother ship appears and sweeps over the rendezvous base at Devil's Tower, the camera cuts to look straight up at the advancing craft as it blocks out the starry night sky. Watch carefully to see some stars passing right through the leading edge of the mother ship, revealing a flaw in the traveling matte effect.