During filming, Larry Storch wanted to do his own stunt and jump from one tree branch to another, but Bill Daily talked him out of it. It was just as well, because when the stunt man did it, it turned out there was a nail sticking out of the tree and the man ripped his arm open.
In the Third and Fourth Season of the show another instrumental theme was also introduced that was played during the shows campy scenes. Simply titled "Mischief", the theme would be heard mainly on outdoor locations - showing the characters attempting to do something such as Jeannie learning to drive, Major Nelson arriving up the driveway, a monkey walking around, or reactions to Doctor Bellows. The theme featured the accompaniment of a sideshow organ, a trombone and bass guitar.
After Jeannie turns him into a human, Sam asks Tony if he has seen his brother on The Jerry Lewis Show (1967). That series premiered on NBC immediately after this episode was broadcast.
The title is based on the song "Fly Me to the Moon" written by Bart Howard in 1954 and became a standard sung by Frank Sinatra.
Reportedly, the producers of Bewitched (1964) accused this show of stealing their episode ideas. In this one, Tony and Roger are working on training a chimpanzee named "Sam", who Jeannie turns into a human. This was seen as a slap at Bewitched, making fun of its main character Samantha. Despite the accusations and the responsive jab, two years later Bewitched had an episode plot that featured a chimp turned into a human.