Rochester was named after Eddie Anderson's character from The Jack Benny Program; besides the name, however, the two characters have nothing in common.
The names of the prince and princess were taken from Carmen Miranda, a fact that was made clear to the audience near the end of the movie.
Unlike the science fiction movies this film parodies, The Jet Benny Show was given a deliberate low-budget appearance; "outer space" was a black backdrop with large white lights poking through it, the spaceship had visible wires, action figures were used for a chase scene, etc. In one scene, the action was replaced with rotoscoped animation.
Jet's vessel, the Maxwell, was named after the Maxwell automobile that Jack Benny claimed to own during sketches on his show.
This movie has been released on VHS videocassette as well as Betamax, but not on DVD.