It's the infamous "Nazi episode" where Kirk and Spock beam down to another copy cat planet to sneak around a Nazi base and outmaneuver the bad guys. Essentially a spy story, the two use all the cliche espionage techniques they learned in "A Piece of the Action" and toss in a MacGyver trick and the Wookie prisoner gag for good measure.
Written by Star Trek producer John Meredyth Lucas because of his fascination with what in the 1960s was recent history, the episode tries to sell the idea that an Earth historian might well see Hitler's way as an efficient way to turn around a struggling culture. It was an easier sell in the 1960s than today, because back then there were a lot of exaggerations about the effectiveness of the Nazi government as a government that have since been debunked (like its 100% employment rate that was only 100% if you discount all those who weren't allowed to work or were killed because they couldn't). But the real problem with the episode is that it takes an hour to say "yes, the Nazis were evil people, but the structure of their government was fundamentally flawed (In other news, the sky is blue).
Still, it was quite bold of the show to tackle the Nazis only about twenty five years since they were in power, and with some outdoor location shooting at the Paramount office building mixed in with quite a few stage sets, the director puts together an exciting little story that has just enough bits to keep it engaging, even if it plays it safe. It's just too bad Lucas writes such a literal version of a Nazi takeover because a more abstract version would be easier to explain and accept. (It would mean the show couldn't use the Nazi costumes raided from Paramount's storage closet or Nazi propaganda footage, but it would take some of the stigma away from what's become perceived as a darker episode than it really
Remastered: This story allows CBS Digital gets to tackle two planets in the same shot, something the original series saved for special occasions (as in, only this episode). Originally, the show reused the planets from "Deadly Years" and "Friday's Child", and they look so close, one could be the other's moon. The upgraded version, with more realistic planets, uses a more three dimensional Enterprise flyby to give them a little more space. Beyond that, they also replace a nuclear missile (which in the original was a shot stolen from "Journey to Babel"), replace a phaser shot and Spock's laser beam, and, of course, redo the ship itself.