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.
Dr. Faraday explains that David hasn't aged because he was moving "beyond the speed of light", according to a "Light Speed Theory". In reality, there is no scientific theory by that name, and no valid theory allows ordinary objects to move "beyond the speed of light". The time dilation effect that Faraday was talking about actually occurs at speeds close to the speed of light but not beyond it, all in accordance with the Special Relativity Theory, which no real scientist would ever call "Light Speed Theory".
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.
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.
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.
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.
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.
When David comes finally reaches home, one of the responding personnel can be heard telling others to sneak up behind him, which would be impossible as the ship is hovering over the water & the steps are just touching the wall at the edge of the river. They would have to be able to walk on water to sneak around behind him.
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.
David traveled a distance of 1120 light years to get to Phaelon and back. Due to the time dilation effect only a few hours passed from his point of view, but 1120 years should have passed on Earth, no matter how fast he was moving exactly. Yet, only 8 years have passed, in violation of the Relativity Theory. It is clearly established that David didn't travel in time to make this possible, since it had been deemed too dangerous, and he couldn't go faster than light (as Faraday mistakenly states at one point), because that is physically impossible.
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 David's mind is unloading images of star charts on to the computer screens, they flash past at a tremendous rate, at least ten a second. One of the scientists says, "These are uncharted systems," but there is no way he could possibly know this given their speed.
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.