According to Bill Mumy, the song that the youngsters were dancing to on set was "Twentieth Century Fox" by the Doors, which was replaced by a generic "rock" instrumental when the episode aired.
Keith Taylor, who plays Edgar here, was also in Miri (1966), which has a similar premise (a society of young people, where no "olders have a place.")
A picture of The Beatles in their Sergeant Pepper's Lonely Hearts Club incarnation can be seen on the wall between 28:01 and 30:44. Clearly the effects of the sixties counter culture can been seen in The Promised Planet, which takes place in 2000, 30 years after the Beatles broke up.
The footage of the Jupiter 2 landing on a concrete landing pad is the same that has been used on several previous season three episodes.
Keith Taylor previously appeared in season one's episode Return From Outer Space.