PLATO’S STEPCHILDREN
AKA: People in authority can be arseholes
Dipping back into the bag of Trek Tropes, we again find long lived aliens who spent some time in ancient Greece, only this time they didn’t influence any human history. Then they came to another planet, exploited the local technology (kironide) to their advantage and proceeded to act like arseholes, using a set of poorly defined powers (
Return To Tomorrow). Then Kirk learns how to use the exact same tech and makes them promise to be nice before flying away, never to return.
This was a bad,
bad episode and IMO has usurped
The Empath as the worst one of TOS.
Both have long, drawn out scenes and feature extensive torture of the regulars, but that at least
Empath had a plot with a clear focus and decent character moments.
Plato’s Stepchildren has none of those and poorly written dialogue to boot! It lurches from lazy plotting (see above) to not one but TWO exposition dumps in the first 5 minutes (Alexander, then Captain’s log) to loosely connected scenes that exist solely to demonstrate how bad the baddies are, before Kirk & Spock turn the tables in the last 2 minutes, make them promise to be nice and leave, having achieved nothing.
Kirk tries to have a “trek” moment with Alexander around 30 minutes in but it’s really not enough to save this episode - it's badly written, boring trash
OTHER THOUGHTS:
- Another distress call to start the episode?

- And just Kirk, Spock and McCoy beam down?

- Yet another episode that feels like a stage play

- The Platonian’s population is 38 – exactly the number that the pinwheel alien in DOTD selected for its combatants – is there is a special significance to this figure?
- Telekentic attacks are great for actors – invisible assailants are a hammy actor’s dream come true!
- Uhura and Chapel are beamed down at 36 minutes in – just because they’re they only regular female characters on the Enterprise, it seems!
- The Platonians are described as “all intellect, no morality” – exactly the morale of the story in The Empath.
AGAIN. 
- Kirk had a communicator stashed in his tunic the whole time? Dare I ask where???

THE KISS
It's been fairly well established the the famous "inter racial kiss" this episode is famous for was not the very first on film or TV, but it's not even the first on Star Trek! The actress who played Elaan (France Nuyen) is of Vietnamese descent and had far more smoochy time with Kirk

Nichelle Nichols does get nice scene right before she and Shatner kiss, but the fact that they are being physically forced to do it robs the scene of any nuance or significance - it's just another form of physical abuse being visited upon them by a bully.
Like the massive exposition dumps earlier, this intentions behind this skit are blatant and have the subtlety of a brick.
On a positive note, this episode features 2 lines which are an ingrained part of my fandom, thanks to Star Trek adverts I saw repeatedly in my youth:
That latter line has so much truth about it...