The girls must submit a photograph and sign a contract which stipulates that if she wins, the winner becomes the Dictator's consort forever and live in his kingdom. The mystery is what the benefactor (who lives on a mysterious dark planet currently orbiting the planet the Robinsons are stuck on) looks like, which interests Will.
Dee Hartford (who was featured in two episodes as the android Verda —"The Android Machine " and "Revolt of the Androids") also guest stars alongside Leonard Stone as the showman's agent who forgot to tell him that in order to get the contract for the pageant she had to agree to a clause that says he sold his soul.
Hartford's character is Nancy Pi Squared and she takes Farnum B.'s orders without batting an eye (and he does bark at her as if she were a slave to his every whim which might ruffle the feathers of feminists). The contract holds an evil spell over Farnum B. whose face turns red when the evil of what he is doing comes over him. Stone provides devious chuckles and a demented look of devilish pleasure when it appears Judy is on the verge of signing.
When Dr. Smith sees that Farnum B. is paid in gold coins whenever he registers a contestant, his greed is kindled and he plots to enter Judy (or, failing that, the Robot) in the contest. With Farnum B.'s cooperation, he manipulates Don and Judy into having a fight, resulting in Judy signing the entry form out of sheer spite.
Don soon reads the contract carefully and is shocked to discover the fine print requiring the winner to become the consort of the Dictator on his planet. He is too late to prevent Judy winning the contest, and even though he and the rest of the Jupiter 2's party escape Farnum B.'s ship, the Dictator and two knights follow them.
The Dictator, having Judy's signed contract, holds some sort of hypnotic spell over her, and is on the verge of drawing her away from the Jupiter 2. The Dictator's nature is revealed when he holds out his hand—he is made of living flame, but Judy is unable to resist his summons. At that moment, snow begins to fall, extinguishing the Dictator and freeing Judy from his grasp.
- June Lockhart and Guy Williams are credited but do not appear in this episode. This was due to their characters being purposely written out of the script because the actors laughed during the filming of "The Great Vegetable Rebellion". In the last episode, "Fugitives in Space", Professor and Maureen Robinson were away from the Jupiter 2 at a radar station, and they are apparently still there.
- Actress Dee Hartford returns to play Nancy Pi Squared. Hardford had played the android, Verda, in two previous episodes.
- When the Robot goes 'drag' to participate in the beauty contest, the voice of the robot is Dee Hartford's voice.
- This was one of Marta Kristen's favorite episodes. Nevertheless, the snow in the final scene was made of hot plastic, which burned her eyes and made her go to the infirmary after shooting.
- When Don drops his wrench in the snow scene, it sounds like it is hitting the hard surface of a soundstage rather than dirt.
- After Will helps Farnum obtain a reptilian contestant for the Beauty Contest, Will, Dr. Smith, and Farnum are watching their payment arrive as gold coins. Excited, Farnum calls Will "Billy" by accident. It was left in the episode this way because the name "William can also be shortened to "Billy."
- The reptilian contestant costume was the same costume used for the beast in The Questing Beast. The costume was originally reddish-orange, but painted green for this episode.
- As with all of the scripts written by Jackson Gillis, this one is straight fantasy with the most tongue-in-check lip service paid to science. As examples, the surface of the planet of the Great Tyrant is supposed to be "radioactive cobalt" and Nancy Pi Squared sells Farnum B's soul in order to secure the Beauty Contest contract.