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.
Other mistake: When Richard Dreyfus rushes to the street to grab the trash can as the trash truck is coming down the street, his family is the only one on the block that has their trash cans out. It's obviously trash day and many of the houses are yet to be serviced by the approaching trash truck. (01:14:30)
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: 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)
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.