The only thing that I will never understand is the popularity of “Balance of Terror”. [...] Again, not to say it's a bad episode, but why is it SO popular?
I would say, why wouldn't one expect it to be among the highest rated? It has a lot to offer: Action, suspense, a strong adversary character, a battle of wits, intra-crew tension, a love story, a heroic act, a tragic death, strong character scenes, an original new spaceship, a look at an alien culture... Pretty strong episode, even if one doesn't personally find it to be the absolute best.