Mirror, Mirror comes as a close second, but my issue with it is how quickly Kirk formulates the theory of being in a parallel universe. Those lines kind of felt like artificially put there to make the watcher understand exactly what is happening.
What other theories should Kirk have considered, that fit the facts as they knew them at that point?
That they are inside some mind trick or under the influence of some malevolent alien? It happened many times before that episode.
They always ran into things that drove the crew mad, delusional or simply degenerate.
The fact that Kirk somehow just guessed the right answer for that situation seemed kind of far-fetched to me.
Well, if we're going to analyze the scene, let's at least have the transcript
Mirror, Mirror wrote:
MCCOY: What is this? Everything's all messed up and changed around, out of place.
UHURA: Captain, what's happened?
MCCOY: No, not everything. That spot, I spilt acid there a year ago. Jim, What in blazes is this?
KIRK: I don't know. It's our Enterprise but it isn't. Maybe
UHURA: Maybe what, Captain?
KIRK: Any of you feel dizzy when we were in the transporter beam?
KIRK: When we first materialised.
SCOTT: I did.
KIRK: It happened twice. First we were in our own transporter chamber, then we faded, and then when we finally materialised, we were here. Wherever this is.
SCOTT: Captain, the transporter chief mentioned a surge of power. The transporter lock might have been affected by the ion storm and we just materialised somewhere else.
KIRK: Yes, here. Not our universe, not our ship. Something parallel. A parallel universe co-existing with ours on another dimensional plane. Everything's duplicated, almost. Another Enterprise. Spock with a beard.
UHURA: Another Captain Kirk, another Doctor McCoy, another
MCCOY: An exchange. If we're here
KIRK: Then our counterparts must have been transporting up at the exact same time. Similar storms on both universes disrupted the circuits. We're here, and they're on our Enterprise. Probably asking the same questions. Are we in another universe, and if so, how do we get back to our own? They'll use the computer, and we have to.
MCCOY: What about the Halkans? We can't let them be destroyed.
I've highlighted what I think are the key pieces of information that Kirk bases his supposition on. Everything being the same, but different, and then the same down to certain details that can't easily be known (how many besides McCoy knew about the acid spot?), the behavior of the transporter beam, and the surge of power because of the storm all suggest that they've accidentally beamed somewhere else, because of the storm. That somewhere else can't really be in their own universe, either. QED.
Yeah, I agree: Kirk's just that good.
He can argue a machine into blowing itself up. He has a genius-level intellect, and he doesn't shrink from the logical conclusion.
It's also worth noting that the theory is confirmed later in the episode, first by the ship's computer as a plausible theory, and then later by Scotty as what's actually happening, when he sets up the transporter to beam them back, as Scotty is able to determine that they don't have much time left to return.
Even if it had been a mind trick, so what? How could they have been any worse off, by following the best escape plan they had before them?