"We've gotta go back, Scotty!"
"Back where, Spock?"
"Back, to the future!"
Trek does time travel for the first time, and other than explaining how it actually works it's a solid outing and a fun episode.
The phenomenon that flings them back in time is described as a
black star, because the term
black hole hadn't been invented yet. On a somewhat related note I recently watched a movie that has a multinational crew on spaceship encounter a black star(no time travel though, it has a different effect). It's a 1963 Czechoslovakian film called
Ikarie XB-1, and it's definitely worth a watch if you're into old sci-fi.
I can never take seriously the implication that contemporary humans would instantly recognize Spock as an alien from another world. Vulcans look too much like humans, I doubt anyone would ever even ask him out of curtesy, but if someone did he could always explain his ears away as a natural defect, an accident or just taking his
Lord of the Rings fandom a bit too seriously.
Even though Kirk has a line implying women on starships are a normal thing, we're also back to "funny" sexism this episode... a computer built on a planet dominated by females, perish the thought! Spock even refuses to use it and does time warp calculations in his head
They apparently use a sonic screwdriver to unlock the computer room, but Kirk gets captured. He sucks at fibbing, which is funny, because he can talk a computer into killing itself, but somehow can't pretend he's from the IT department and confuse a human security guard with his computer lingo?
As Kirk is captured, Spock's being in command streak continues.