"Miri" is the template for countless episodes throughout the franchise, with so many examples I hesitate to even begin listing them. And that template is: crew comes across planet with a population dying of a pandemic, must find a cure.
The other distinguishing factor to the episode is that it's one of many from the series that finds a way of putting the crew into vaguely contemporary surroundings for viewers. In this instance, it's the 1960s, for some reason, on an alien planet that matches Earth in every other way, except that the population is a bunch of kids who are the only survivors because the disease killing everyone turns fatal afterward.
The title character is the leading figure of this community, by the way.
Another distinguishing characteristic/precedent is the curious community these children have formed, their own speech patterns, as later revisited in "Damok" in The Next Generation and "Nemesis" in Voyager. At least one of those, no doubt, seems a lot less ridiculous, I'm sure, in comparison. (Child actors were generally terrible back then. And as such, were given terrible material.)
Is Yeoman Rand once again put in the spotlight? Of course she is. In these early episodes, she's practically the fourth lead, behind the familiar trio. Is Spock, meanwhile, commenting on the advantages of his Vulcan physiology? Is McCoy busy trying to cure the pandemic? Is Kirk busy lusting after Rand, and taking the opportunity to freak out because that's a side-effect of the disease? Of course of course of course!
I'm saying is, if you want an episode that probably helps people dismiss the whole franchise based on one experience, this would probably be a pretty good pick. Later versions did the story better. But anyone who saw this episode, and probably really only just this episode, thought the whole thing was a joke. Which makes "Miri" a prime example of why the series really did have its challenges to overcome, well before the third season, in finding a lasting legacy. It was certainly there, and paradoxically even in this very episode.
But this is an episode that aside from the good it helped create, is something bad you can probably completely overlook and be a better fan for it.
Scotty, Sulu, and Uhura do not appear in "Miri."
Although, one giant bonus of the whole sorry experience is Phil Morris's first appearance in the franchise. Here he's just a kid. His biggest spotlight would be in Voyager's "One Small Step."
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Grace Lee Whitney
Memory Alpha summary