After it's revealed that David has been missing for 4.4 hours in analysis mode on Phaelon, one of the technicians says, "Light speed theory" but the words aren't consistent with the movement of his lips.
When David is interviewed at the hospital, a woman asks him what happened to him at the woods after his brother scares him. David replies "I chased him for a while, then I reached this cliff... I know I fell". Actually, he made only a few steps after his brother, then turned and walked toward the ravine, with no cliffs in sight. He seems confused and distracted during the interview, which is hardly surprising under the circumstances.
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.
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 drawbridge. 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.
Right before David sets out to meet up with Jeff in the woods, he's out on the front lawn feeding Bruiser. He 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.
In 1986 when David is reunited with his parents at the front doorstep of their new home, Bill places his left hand near Bruiser at one point. But in the following shot where David faints on Helen's lap we can see Bill's right hand near Bruiser instead.
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.
Within moments of being confined to his room at NASA headquarters, David meets Carolyn and R.A.L.F. When Carolyn first pokes her head into the room, her hand repositions itself on the door frame as the shot changes, moving closer to the light switch plate.
When David is in the ship at the NASA hangar, just as Dr. Faraday tells 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.
As David and the ship are leaving the NASA hangar, 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.
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.
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).
When David and Max are lost and in need of directions, they spot a red Mustang cruising along. The Mustang is within throwing distance of a T junction at first, but then in the following shot it's suddenly about a quarter mile away from it.
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.
After David is shown the collection of aliens aboard the ship, one of them eats his NASA cap. Just a few minutes later we see the same hat on the floor in front of the chair just before his mind transfer.
When David first looks at the road map on board the ship, he chews a piece of the Nestle Crunch bar he bought at the gas station. The next shot shows the bar close-up, without a bite taken out of it. When the camera cuts back to a wide shot, a large bite is missing.
When RALF enters David's room for the first time, its yellow flasher shuts off as soon as the unit stops moving. In the next shot, when the door reopens and Carolyn steps in, RALF's flasher is on again for a split second.
After David agrees to be taken to NASA headquarters for a 48 hour observance, Dr. Faraday winks at him, and in the left lens of his glasses (from the viewer's perspective) we can see the camera operator at work.
When the alien craft speeds away from the NASA base, its slipstream tears off the roof of a small booth. But the wake also should sweep the people in its flight path down to the ground; it is too close for that not to happen.
After David's ship breaks free and exits the hangar, he orders Max to take him twenty miles away. Back at the tracking room a technician informs Dr. Faraday that the ship has gone 20 miles straight up, but the target altitude indicated on the screen reads 184,800 feet - a 35 mile distance.
When the starship is falling out of control, it's falling into a region filled with snowy mountains. The radar map clearly shows the ship over the southern coast of Alaska; San Francisco and Seattle are in the lower part of the radar map. Since the ship flew from Florida to Alaska in what appears to be a few minutes, many viewers think the ship is over the Gulf of Mexico or the Florida coast. Later scenes confirm that the ship really can move that fast.
When Max stops 20 miles from NASA and David leaves the ship to pee, he goes behind an orange tree with ripe oranges growing on it. Oranges ripen during the winter months, but the movie takes place in July.
The goof item below may give away important plot points.
According to the information in David's brain, he traveled to Phaelon and back in 4.4 hours, while 8 years had passed on Earth. Dr. Faraday explains that according to "Light Speed Theory" David has "traveled beyond the speed of light", and "time slows down when you approach the speed of light." Light Speed Theory does not exist. No scientific theory allows ordinary objects, such as David's body, to travel beyond the speed of light. It might be argued that the movie's physical reality or scientific knowledge are different from ours, but nothing else in the movie supports that claim. Dr. Faraday's statement that time slows down when you approach the speed of light is basically correct within the Relativity Theory, but if Phaelon was 560 light years away, David should've returned 1120 years later, not 8. To generate a time lag of 8 years, Phaelon would have to be about 4 light years away.