[TOS] Season 3, Episode 16: The Mark of Gideon
This episode is a particularly nice showcase for Spock, but overall I think it succeeds not because of plot or theme, but atmosphere. Kirk wandering the empty Enterprise, and the general sense of mystery, is very effective.
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Read more at Memory Alpha
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Notes:

Apparently, Kirk’s on a fake Enterprise. I like how this episode makes fun of bureaucracies, and how people talk when they’re trying to be political and diplomatic.

Whenever Kirk asks about the planet he was beaming to, or anything else about what’s going on, this lady has no idea what he’s talking about.

The lady passes out and the leader of the planet shows up. It isn’t really a surprise that he’s behind this whole thing.

They live on a planet that was once considered a paradise. Something in the air made people live super long lives, they had no diseases, and their organs regenerate. But now it’s miserable because it’s too crowded.

Kirk asks why they didn’t just use birth control or something, and the leader’s response is that people just love life too much.

They needed Kirk because he had a disease that works on their planet. They need it to kill some people. The lady might be the first victim. The alien’s worldview is a little confusing.

Then Spock beams to the fake ship and very quickly realizes what’s going on. He just starts neck pinching everyone.
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