#47: Wink of an Eye
In case you forgot: The Enterprise answers a distress call from a planet, only to find it complete devoid of life. Or so they think: turns out the life there moves so fast that everyone is invisible to the crew of the Enterprise. Kirk gets kidnapped by one of these aliens for the purposes of breeding, and the entire Enterprise has been hijacked.
Aliens who pass through time at an entirely different rate than humans do is a cool idea. The way it's implemented is a bit silly, but if you can accept that, then the whole episode plays out pretty nicely. I have to commend the directors/producers for sneaking crap past the radar on this one: the scene with Kirk putting his boots back on and Deela brushing her hair is such an obvious "THEY JUST DID THE NASTY" shot, and yet the censors never noticed it?
McCoy and Spock figure out what's going on fairly quickly, all things considered: there isn't much idiot ball going on in this episode.
All that, said, there's a pretty big "if" up there. The idea that radiation speeds up time and makes you invisible is one of the sillier conceits in the show. Wink of an Eye is fun enough but the goofiness of that particular conceit hangs over the whole thing for me.
I'm also not sure how I feel about those alien fashion choices. Tin foil scrubs and half of a jumpsuit? Not a look that's aged well.