If this episode were redone, chances are more people would care how traumatic it probably was for Kirk. Also, the villain's name is Kodos. And of course there is later a Klingon named Kang. And now you know the origins of the names for those silly green aliens on The Simpsons.
But "Conscience of the King," other than sporting another early Shakespeare reference in the title of an episode, is about a mass murderer trying to run away from his horrendous past. I'm certain this was quite a significant topic for people in the 1960s, when Nazis were still actively being brought to justice for their crimes during WWII. As such, I will leave it in that context, rather than in direct reference to the later Deep Space Nine classic "Duet." But these episodes are still similar in that respect.
What does Kirk's past have to do with it? There was a colony he spent part of his youth growing up on (famously, as Star Trek IV: The Voyage Home and Star Trek make plain, he's from Iowa), and this colony ceased to be thanks to Kodos the Executioner. Whose name tells you everything you need to know about him.
The problem is, he escapes justice and later becomes an actor. Now, the direct line from the title comes from Hamlet, and evokes comparisons that are not really all that accurate. The conscience in Hamlet has to do with one death, not genocide. You'll remember, though, that in slightly more direct line, there's a play involved wherein said conscience is supposed to be exposed. And so that's more or less this episode, a thin borrowing of a few elements from classic literature and real world events.
Not especially the most elegant. I'd say the whole thing could really be improved. And I'll basically leave it at that.
Striving for greatness and profundity. Maybe you think this episode reached these lofty goals. But I'd say this was a stepping stone to others that did. But certainly not the article itself.
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Memory Alpha summary