This is the first episode of the series to be broadcast. It's not the first episode to be filmed, or the second or third...As with what happened to a number of later Voyager episodes from its first and second seasons, decisions were made as to what could possibly best represent this outlandish new science fiction experiment to small screen audiences, and this relatively straightforward episode got the nod.
And so, it's a little hard to say what was the "first" appearance for most of the original series cast. Aside from Spock, everything's out of order anyway.
But surprisingly, the first episode of the series and indeed entire franchise to be aired was not a Kirk episode. That's right! It's actually a "Bones" McCoy episode, one of several to remark on some previous aspect of his life (as is usually the case, an old flame). It's a gimmick of a premise that would turn up repeatedly in the franchise. As such though, there's not a lot to recommend about "Man Trap" except for its luck in being aired first.
It's actually not a bad way to introduce the series, either, even if late in the debut season the basic story is vastly improved in "Devil in the Dark." This is the "salt vampire" episode, featuring a distinctively alien creature who would end up appearing in the post-credits sequence throughout the rest of the series (and now looks either like a Twilight Zone creation or something out of The X-Files, because it's certainly not representative of what Star Trek aliens would look like as a rule).
The thrust of the story is that McCoy's former flame is visiting but seems to be tangled up in a murder mystery. McCoy struggles to the end of the episode (another element that is later echoed, in "City on the Edge of Forever," perhaps the all-time standard for great original series episodes) how to handle the emerging truth, that his old lover is gone.
As with "Devil in the Dark," the villain of the episode is actually sympathetic. Like a lot of fictional alien species, the salt vampire is the last of its kind. As regards the opposite of the conclusions reached in Star Trek IV: The Voyage Home, the crew ultimately has no qualms of making the species extinct, mostly because it can't come up with a better solution.
The main reason for that is because the salt vampire is also a shape-shifter. Shape-shifters came up a number of times in original series lore, including in the later Animated Series and Star Trek VI: The Undiscovered Country. Of course, they're most famous in the franchise in the form (heh) of Odo in Deep Space Nine. As with a number of these precedents (including the androids and even the holodecks, not to mention Q), the connections are never made between eras other than that the concept had been used before. But as far as that goes, this first of all episodes also helps establish one of the recurring elements of the whole franchise, so if you want to watch the episode on that basis, that's just as well.
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Grace Lee Whitney
Memory Alpha summary