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.
Continuity mistake: When Richard Dreyfus has his first UFO encounter at the railway crossing, all the gauges in his truck go wild and the contents of the glove box comes flying out. After the encounter finishes, and the vehicle's power comes back, Dreyfus starts the engine and drives off. Miraculously, the interior of the truck has tidied itself and restored the glove box contents to their proper place.
Factual error: Early in the movie there's a scene that takes place at the FAA air traffic control center. As the film's other scenes are set in Muncie, Indiana, this ATC center is presumably (and correctly) in Indianapolis, yet, after the UFOs nearly collide with the TWA and Air East flights, the controllers are talking about "restricted area 2508". The "real" R-2508 is actually out in California/Nevada.
Visible crew/equipment: When the little boy is looking out the window of the farmhouse toward the sky to see the incoming spaceships (where he says "toys" rather excitedly), as the camera closes in toward him you can see the shadow of the camera/crane on the right side of the screen. The shadow changes as the camera zooms in.
Continuity mistake: As Ronnie backs out of the driveway, she knocks a Big Wheel across the road. She takes off as Roy falls off the hood and lands beside it. It disappears after he stands up and the angle changes.
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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.
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).