Due to the post-war German ban on Nazi-related imagery and paraphernalia, this was the only Star Trek episode that was not shown on German TV until mid-1990's, when these restrictions were gradually relaxed to allow for artistic expression.
The name of the planet Zeon is a variation of the word "Zion", a Hebrew term, as in Mount Zion, near the city of Jerusalem. The names of the Zeons: Isak, Davod and Abrom are obvious references to Isaac, David and Abraham, traditional Hebrew biblical names.
The "leader principle" Kirk mentions at the end of the episode was a foundation of the leadership in Nazi Germany. Known in German as "Führerprinzip", it essentially can be described as a state of law in which there are no laws above those of the Führer, and that the government must obey and enforce such laws.
This episode was filmed on the 25th anniversary of the Holocaust. William Shatner and Leonard Nimoy, both being of Jewish backgrounds, felt compelled that Kirk (disguised as an S.S. Obersturmführer) and Spock (disguised as a member of the Gestapo) should defeat the Nazi Reich on planets Ekos and Zeon.
The Schulberg Building (formerly, the Directors Building) and the Lubitsch Building (formerly, the Producers Building), both located on the Paramount Studios lot, were used for the exterior shots of the Ekosian Nazi headquarters complex.