I'd like to start this post by extending a belated Happy Birthday to William Shatner, who turned 90 yesterday.
Mike Godwin didn't come up with his famous 'law' until 1990, but a variant of it as that as any science fiction franchise continues, the chances of a discussion or comparison to the Nazis increases. It only took Doctor Who two stories - the Daleks are very much a Nazi metaphor - and now we have a very explicit Star Trek comparison, symbology and all.
Indeed, this episode was not aired in Germany until 1996; there is no ban on the use of Nazi symbols in television and film for dramatic purposes, but the German networks just chose not to broadcast it - it was after all only 23 years in the past and a felt bit too early for the subject to be covered in light entertainment.
Heading towards the planet Ekos to pick up a cultural ambassador who was one of Kirk's instructors at the Academy (he knows a lot of people, our Captain does), the Enterprise gets shot at by a nuclear missile. This is successfully dealt with and it is clear that something has gone badly wrong with Ekos, even more so after Kirk and Spock beam down to discover the place is basically Nazi Germany, with a plan to exterminate another race in the same system.
This doesn't exactly win any awards for subtlety. You've got a Nazi government planning a Final Solution against a planet called Zeon, whose people in the planet have names like Isak and Abrom. It's also worth pointing out that Shatner and Nimoy are/were Jewish - wearing SS uniforms is an interesting experience for anyone, but I'd imagine it is more so if you're a member of that particular people. As indeed is Walter Koenig who plays Chekov - his family fled Lithuania because of antisemitism.
The Ekosians are costumed in uniforms literally pulled out of the Paramount wardrobe department (they made a lot of war films) and generally with mis-matched insignia. Indeed, this episode was filmed in Paramount's offices with the corridors redecorated.
Kirk and Spock end up getting captured, losing their shirts and getting whipped with some unconvincing looking injuries; I suppose that the network wouldn't have allowed more realistic whipping. We do get a rather funny scene where Spock has to stand on Kirk's injured back to create a laser using a lightbulb... it's a pretty ridiculous scene in general, but I'm glad they thought of that detail. The leads all get good material.
The main characters then end up working with the resistance to infiltrate the Chancellery to get at the former ambassador who has now become another Hitler, although his deputy is now pretty much running the show. The overall reveal of his motivations for doing this is a bit unconvincing in the light of further historical analysis of Nazi Germany - it wasn't as efficient as thought - and to be honest, could have been written better. I get a feeling that this whole episode is a bit rushed - indeed it was trimmed in the edit - with key bits skipped over. Brevity is not always the soul of wit.
Where the episode does work is in the whole espionage/skulduggery department; I am very much reminded of 1960s Mission: Impossible, which of course Leonard Nimoy was in. Moles, infiltrating an enemy headquarters in purloined uniform and getting past the guards through sheer bluster, is the classic bread and butter of these sorts of stories - I generally enjoy them a lot. The climax is pure Mission: Impossible; the IMF would rarely kill their targets directly, but getting them to shoot each other was perfectly fine.
The episode ends in a rather perfunctory manner and it's left assumed that the hatred engineered against the Zeon people will magically go away. History tells us that really isn't the case.
Distinctly average and perhaps too unsubtle. This might have worked a lot better as a two-parter too.