The look of the character Galt was modeled after Ming the Merciless, the archenemy from the Flash Gordon comic strip.
During an interview, Angelique Pettyjohn said that when she first auditioned for the role of Shahna, she admitted to the producers that she didn't think she fit the character. When they asked why, she said the script describes her as an Amazon, but at 5'6", Pettyjohn said she's hardly an Amazon. The producers all laughed and said "Look, honey, next to Shatner, you'll look like an Amazon."
When Joseph Ruskin saw that his costume consisted of a long black floor-length robe, he came up with the idea of walking in an extremely fluid way (known as "glide stepping" by marching bands). He thought that combined with the robe, it might make the viewer wonder if he was even a biped humanoid, or perhaps had some other means of movement.
The producers interrupted filming of this episode to tell the cast and crew that the show had been cancelled. Everyone was depressed throughout the rest of production. But then fans started protesting and writing letters until NBC decided to keep it on for another season.
A triskelion is an ancient symbol used in Greek, Roman and Celtic cultures. It was originally three spiral but evolved into three legs, as seen in the flag of the Isle of Man. The symbol shown on the planet is a geometric version of this design.
Bob Johnson: Johnson, voice of one of the Providers, was one of America's most famous voices for a few years: he was the tape recorded voice that gave the Impossible Missions Force its assignments at the beginning of most episodes of Mission: Impossible (1966). Mission was filmed next door to the Star Trek set, and actors from the series would often wander over to see what was happening on the Enterprise. Johnson previously did voice work on the first Star Trek pilot, The Cage (1966).