When David's parents pull up to their house in the beginning of the movie, the song playing on the car radio is "You're The One That I Want" from "Grease", also directed by Randal Kleiser.
The ship used in the movie can be found in a boneyard at the Disney MGM Studios Theme Park at Walt Disney World in Florida. It can be seen on the studio tour.
The tee shirt worn by the girl at the restroom is for EPCOT Center, the then-new Disney theme park in Florida. Her brother is wearing a Miami Vice tee shirt.
MAX, the ship computer speaks in Bulgarian. When David enters the ship and takes the pilot seat MAX says "Vnimanie! Oblegni se! Chui me!" which means "Attention! Sit back! Listen to me!"
When MAX, the ship computer, is describing the animals he has on board, he said "That is a Feenastarus from the Pixar Elliptic". This was five years before Pixar, a fledgling special effects computer group at the time, teamed up with Disney, who produced this film.
In a deleted scene David returns to his home, now occupied by a middle-aged couple. After he describes his family the woman believes that this is the missing child the previous owners talked about. In an attempt to have David remain calm until the Police arrive the woman prepares a plate of snacks. David, not being hungry and believing everything to be a hoax runs into the woman as he runs upstairs to his former bedroom. This explains the scene in which David runs into the woman carrying the plate of snacks (Who was previously empty handed). This also explains the scene at the Police station in which the officer says to David "Not hungry, huh?".
Not originally a Disney movie, the film was being made independently when midway through production the main production company, Producers Sales Organisation (PSO) collapsed. Walt Disney acquired the production in a liquidation sale, picking up all film rights for this film and several others, and also putting up the finance for its completion.
When escaping the NASA facility, MAX and David travel "precisely 20 miles from point of origin" in approximately 35 seconds. This is equivalent to a speed of 2,057 miles per hour.
The trivia items below may give away important plot points.
David's flight to Phaelon and back took "4.4 Solar Hours," while 8 years have passed on Earth, indicating that time was slowed down for David by a factor of about 16,000, which corresponds to a speed of about 99.9999998% the speed of light.