The good news is that Gene Roddenberry thought this episode was crap, too. Adrian Spies never wrote for TOS again—not just because the story was weak, but apparently because he didn't really have a solid grasp of the teleplay format either.
But there is just so much still wrong in this episode: Kirk putting the moves on a confirmed underage girl (even though the actress playing her was obviously significantly older, still....eugh), the Power Trio and company being outwitted by a bunch of prepubescents, the terrible writing for the kids ("BONK! BONK!").
The kids are the worst. It's not their acting, either, even if child acting is legendary. They are just written so poorly. The episode lets us know that these "kid" are hundreds of years old, at the youngest. And yet being alive for hundreds (in some cases thousands) of years and watching friends and family succumb to the virus has not given them the kind of otherworldly "wise beyond their apparent years" aura one would expect. They are basically stuck in an awful arrested development scenario, a permanent prepubescence that has no bearing on the awful things they've endured.
The special ick in this episode is, of course, Kirk putting the moves on Miri. Not at all comfortable to watch.