In case you forgot: This is the episode where Kirk and Uhura kiss. They kiss because a race of beings with god-like telekinetic powers are bored and need something to play with.
Alexander is one of my favorite alien-of-the-week characters. He's the only person left on this planet with anything resembling a moral compass, which is impressive considering he's spent who knows how many years being the butt of everyone's jokes. That's usually the stuff school shootings are made of. It's Alexander that really helps this episode make the jump from "okay" to "good."
It's also a nice touch that the aliens' powers are hindrance to their development in other ways: their eugenic focus on mental prowess has been at the cost of the robustness of their physical bodies (hence why they want a skilled doctor like McCoy around).
Otherwise, the Greek theme comes off as a bit unnecessary. There is nothing about their lives that is inherent to Plato or his Republic; at least Apollo in "Who Mourns for Adonais?" was, literally, Apollo and thus had grown used to Greek trappings. So much of the episode is watching Kirk and Spock being tormented by Parmen, the ruler of the planet, that it makes for some filler that is a YMMV situation; for me, there wasn't much mileage to be had at all.
The crowning sin of this episode, though, is the end. Kirk and Spock manage to get some telekinetic powers of their own (it's in the food) so they can stand up to Parmen and give him a lecture about ethics and how Starfleet and the Federation will be back to check up on them, but...that's it. These people are probably some of the more vile alien races encountered and Kirk just lets them get away with it? That is the difference between a good episode and a great episode.