I'll keep this brief, as I feel this episode offers very little to analyze critically.
I found this episode to be sloppily plotted. The characters encounter a peculiar issue (as they usually do) and the entire episode seems to bank upon our being interested in the extreme peculiarity of that issue. This is lazy and unreliable.
The issue at hand is the Enterprise discovering an earth-like planet (looks exactly like earth, an issue left completely and shockingly unresovled) that has been deserted for centuries ... except for the children, who have survived for hundreds of years. The action of the episode involves the crew stumbling upon crumbs of information to finally (and arbitrarily) conclude that the inhabitants of this planet created a virus, the effects of which preserve the life of the children and brutally transform and kill the adults.
The only thing resembling drama stems from the fact that the children they have met will eventually reach puberty and the virus will have its way on them. Meanwhile, the crew is becoming infected, and has only a limited window of sanity to produce an antidote. The resolution of the situation is so un-earned and unsatisfying I'm left breathless. Is this Star Trek?
McCoy finds some research papers and creates an antidote -- if he's wrong, it could kill him -- which he tests on himself. It works and saves everyone. Gee, that seemed rather easy. The only other complication (not to suggest that more "complications" would ensure better drama) is the lost-boys-like child congregation's disdain for the crew leading them to steal their communicators. Which, really, births McCoy's necessity to test the unconfirmed antidote on himself. So, it's really just the one thing. There's a moderately nice but unfortunately forgettable plea from Kirk for the children's help.
Other than that, all I can say is that Kirk's relationship with the puberty approaching Miri is a bit uncomfortable. Oh, and that this episode has two -- count 'em, two -- out of place or noteworthy Spock lines. "It could be a beaker full of death" and my personal favorite:
"That little girl is at least three hundred years older than you are, yeoman ... think about it."