In the scene where David is watching Jennifer through a telescope, the song Lovefire is playing from the movie Roller Boogie. Flight Of The Navigator starts out in July of 1978, but Roller Boogie didn't come out until December of 1979.
When David and Max are flying back to Ft. Lauderdale, supposedly following I-95, they pass a road sign that indicates Miami is 25 miles away, and Ft. Lauderdale is 58 miles away. Since Miami is south of Ft. Lauderdale, this means that they are flying north and located to the south of Miami, while I-95 exists only to the north of Miami. Subsequent scene confirms that they are indeed flying north, since they pass Miami Beach on the left. However, nothing indicates that they were ever flying along I-95, so it's more likely that they simply misread the map and reached that road sign by luck. Previous dialogs do indicate that both David and Max are very bad at navigation.
When David is interviewed at the hospital, a lady asks him what happened to him at the woods after getting scared by his brother. David replies: "I chased him for a while, then I reached this cliff... I know I fell". Actually, he made only a couple of steps after his brother (hardly a "while"), then turned and walked toward the ravine, with no "cliffs" in sight. He does seem to be confused and distracted during the interview, which is hardly surprising under the circumstances.
When David is making his descent into Miami at the end, his mom is in her home surrounded by NASA guys watching "The Price is Right" and it is bright and sunny during the middle of the day. After a quick dialogue back in the spacecraft, it cuts back to his mom in the house and it's pitch black. "The Price is Right" is only an hour long.
MAX, the space pod, is bigger on the inside than on the outside (this is evident by looking at the ship's hatch: the bottom of the hatch is near the bottom of the ship, but the inside has room for retractable engines, controls, and a pilot's chair). However, this may be deliberate as classic science fiction had ships that were larger inside than outside.
While first looking at the road map on board the ship, David is shown chewing a piece of the Nestle Crunch bar that he bought at the gas station. The next shot shows the bar close-up, but in that shot a bite hasn't been taken out of it yet. When the camera cuts back to a wide shot, the bar once again has large bite missing from it.
When RALF enters David's room for the first time, its yellow flasher shuts off as soon as the unit stops moving, but in the next shot where the door reopens and Carolyn steps in, RALF's flasher is on again for a split second.
In the scene where David is outside the ship in the Florida cow field, the shadow of the framework holding up the ship is visible when the ship is viewed from the air. You can also see several dents in the ship's finish.
At the beginning of the movie, David falls into a deep ravine. However, south Florida is totally flat - if you fall more than 2 feet below ground, you are in a canal in water. Also, the vegetation is not south Florida either, so this scene was not shot in south Florida.
It is often claimed that when the starship is falling out of control, it is over the Gulf of Mexico or the Florida coast, which is contradicted by the fact that it's falling into a region filled with snowy mountains. However, the radar map clearly shows that the ship is actually over the southern coast of Alaska (San Francisco and Seattle can be seen in the lower part of the radar map), where such mountains are abundant. The confusion is due to the fact that the ship has flown from Florida to Alaska in what appears to be just a couple of minutes. Later scenes confirm that it really can move that fast.
When Max stops 20 miles from NASA and David leaves the ship to answer the call of nature, he goes behind an orange tree with ripe oranges growing on it. Oranges ripen during the winter months, but the movie is supposed to take place in July.
The goof item below may give away important plot points.
According to the information in David's brain he had traveled to Phaelon and back in 4.4 hours, during which 8 years had passed on Earth. Dr. Faraday explains this by saying that David has "traveled beyond the speed of light" and also that "time slows down when you approach the speed of light", all, supposedly, according to "Light Speed Theory". In reality, there is no scientific theory by that name, although it's sometimes (wrongly) used as a reference to the Special Theory of Relativity. In any case, no scientific theory allows ordinary objects (such as David's body) to travel "beyond the speed of light". It might be argued that the physical reality (or the scientific knowledge) in the movie is different from ours, but nothing else in the movie supports such a claim. The second of Dr. Faraday's statements (that time slows down when you approach the speed of light) is basically correct within the Relativity Theory, but according to it David should have returned 1120 years later, not 8, given the distance of 560 light years to Phaelon. To generate a time lag of eight years, Phaelon has to be about 4 light years away, not 560.