Continuity mistake: As David and the ship are leaving the NASA hanger, the straps that are holding the ship down start to break. From the shot outside the ship, you can plainly see the straps hanging on the front off the ship, but from inside the ship looking out the front "viewscreen" you see a clear picture, with no straps obstructing the view.
Continuity mistake: After David has relieved himself, he and Max start a heated conversation about why the computer hadn't returned David back to his own time; a herd of cows grazes nearby. Towards the end of the debate, a cow can be seen near the ship's hatch in a close-up; in a wide shot, the cow is gone; and in a second close-up, the cow stands near the hatch again.
Continuity mistake: When Dr. Faraday and the radar technicians are monitoring David's ship as it free falls towards the U.S. west coast, take a look at their glasses and you'll notice how a map of Japan is being reflected instead (needless to say, the exact same image is reflected three minutes later when the ship enters Tokyo airspace).
Continuity mistake: When David is in the ship at the NASA hanger, just as Dr. Farraday asks him to get out of the ship, the door closes. From outside the ship, the interior is pitch black, but in the very next shot from inside the ship, it is lit up from the front "viewscreen" and various lights on the wall, which should have been visible as the door closed.
Continuity mistake: The three-digit code on the police car which takes David to his parents' new home changes. Just before it parks by the house, it makes a left turn near the highway. Here we can see its number is 442. But when Detective Banks exits the car, the number is partially visible - with the last two digits being 51 instead of 42.
Continuity mistake: When Dr. Faraday is talking to David and his family along the New River in Ft. Lauderdale about going to the NASA facility, in the beginning of conversation up until when David says "no" the Andrews Ave. draw bridge in the background is down. When Dr. Faraday convinces David to go to find out where he's been 30 seconds later, the bridge is open/up and is closing/going down during the rest of the conversation.
Continuity mistake: Right before David sets out to meet up with Jeff in the woods, he's out on the front lawn feeding Bruiser. It eats everything on the tray, save for a couple of pieces - but when Helen calls for David from the patio in the following shot, the tray is nearly filled with dog food all of a sudden.
Continuity mistake: When David goes to his room early in the movie (in 1978), if you look closely you can pick up what looks like a football card wrapper on the shelf on the left side of his room, near the white helmet and behind David's Dad. Comparing to known wrappers, this one was issued in 1985.
Continuity mistake: After David contacts Jeff from a payphone, he heads back toward the ship where a father is getting ready to snap a family photo. Behind the gas pumps is a Dodge Caravan with closed doors. Once the ship lifts off a few seconds later, you can see how the van's rear passenger door has managed to open up all by itself.