The infamous "Nazi episode" is actually not that bad. Okay, the premise is ridiculous, but grant it that and the story is compellingly dramatic and moves along nicely, which is more than you can say for some episodes.

It also shows that the Enterprise has the capability to dress crew in military uniforms of any historical era at the drop of a hat. The Enterprise-D of The Next Generation era had an explicit costuming department to dress away teams appropriately, but this is the closest we come to seeing such a thing in operation in the classic era.

Transcript

1
Captain's log, Stardate 2534.0. Cultural observer John Gill has been missing on Ekos for 6 months. The system contains a second inhabited planet, Zeon.
Uhura: No response from Ekos, captain.
Kirk: Spock, allons-y!
2
Kirk: Inject subcutaneous transponders, in case we lose our communicators.
McCoy: Remind me again why we don't do this on every mission?
3
Ekosian soldier: March, Zeon pig!
Kirk: Nazis! I hate these guys.
4
TV: The Führer has announced the Final Decision: death to Zeon!
Kirk: It's John Gill! He's turned Ekos into a planet of Nazis!
Spock: Incredible. He has violated the Prime Directive even more flagrantly than you.
5
Caption: They steal Nazi uniforms.
{Spock and Kirk in snappy Nazi uniforms}
Kirk: Snappy!
6
Caption: It fails.
{Spock and Kirk captured by Nazis}
Ekosian Nazi Officer: Zeon schweinhund spies!
SFX: Whip! Whip!
7
{Kirk and Spock in a prison cell}
Kirk: Let's cut the transponders out of our arms and use them to MacGyver an escape!
Spock: Or we could use them to call for help.
Kirk: You're no fun at all.
8
Isak: Thanks for saving me. I'll take you to the underground resistance.
Kirk: Where is it?
Isak: Underground.
Spock: Most logical.
9
Isak: Daras here is a decorated Ekosian hero, but sympathetic to the Zeon plight.
Daras: I can get you close to the Führer. He's giving a speech tonight.
10
Kirk: Uhura, beam Dr McCoy down.
Uhura: {over communicator} He wants to know if there's a PLAGUE?
Kirk: No, but he can dress as a Gestapo Colonel.
Uhura: He'll be right down.
11
Kirk: Gill is drugged. Give him another stimulant.
McCoy: No, it'll probably kill him!
Kirk: Okay... uh... leave the room. And leave the hypo here.
McCoy: Sure!
12
Kirk: Why, John, why??
Gill: Ekos... divided. Wanted to... unite planet. Give... good example society.
Kirk: The Nazis??
Gill: Eh, live and learn. {dies}
SFX: Die