It seems moments before the start of the show, the ship was being sucked into a black hole, an effect that would’ve been too expensive to let us see. Kirk instructed the ship to use its full engines in reverse to escape, but the rubber band effect of them escaping the black hole’s gravity was enough to catapult them THROUGH TIME. This is the second time the Enterprise has traveled back in time, and the secret seems to be just “drive backwards very fast.”
The ship lands back in the 1960s over an American air force base, of all things, and we’re treated to plenty of stock footage of jets taking off as they scramble to pursue the UFO. The ship is pursued by a jet, and Kirk decides to use a tractor beam on the ship to stop it from shooting them with a nuclear missile, which I suppose all fighter jets have. So in the midst of Cold War paranoia, our response to something we didn’t understand was to blast it with nukes?
Spock, diligent as ever, explains to Kirk a few moments later that the jet’s shoddy 20th century craftsmanship will be unable to withstand the force of the tractor beam. So within moments of arriving in the ’60s, the Enterprise has already made themselves out to be hostile aliens with a death ray.
In an effort to cover his ass, Kirk orders the jet’s pilot beamed aboard. Hilarious misunderstandings ensue as Kirk has to explain to the pilot, Captain John Christopher, about how the Enterprise crew come from the future, and how they employ aliens, and how they treat women with ever so slightly more equality than they do on a 1960s air base. Captain Christopher takes everything in pretty well, and by the time they show him the machine that can make any kind of soup, he’s bored. He asks to return to his family.
Kirk, of course, won’t let the guy go home because he knows too much about the future, and they don’t want him mucking up the timeline. Well, not any more than Kirk himself already has. Christopher counters with the idea that they’ve already messed up history with his disappearance. Spock informs him, with his best beside manner, that history doesn’t end up remembering him for anything. “We’re sorry you can’t ever go back to your old life, but if it’s any consolation, you wouldn’t have actually mattered.”
Nevertheless, they need to beam down to the air base and steal the footage Christopher’s plane took of the Enterprise. Sulu and Kirk go to the base and start looking for the tapes, giggling and pointing at quaint 20th century technology, like cork boards. As they’re stealing a few military secrets, a guard corners them and holds them at gunpoint. Panicking, Kirk orders the guard beamed up, further increasing the damage they’ve done to history. Kirk with time travel is like a kid with a BB gun shooting animals; he doesn’t seem to understand that his actions have consequences.
Before they can make a clean escape with the tapes, some officers take Kirk prisoner, after a long, Three Stooges-esque fight. I think Kirk’s signature fighting move must be “swinging on a tree branch or door jamb and kicking a guy.” Maybe a new martial art. Kirk-rate?
Kirk is interrogated by the military, who don’t buy his stories about spaceships and lasers for some reason. The crew comes to his rescue, and just when all is well again, Christopher steals a phaser and demands he be taken home. Spock replies that he made an error in his earlier research, and actually Christopher’s son leads a crucial first mission to Saturn. So even while trying to fix the timeline, Spock damages the timeline by giving Christopher foreknowledge on his son, who will be way more successful than him.
Anyway, the phaser incident is forgotten, all is forgiven, and the Enterprise makes a quick hop back before returning to the future, so they can drop Christopher and the guard off at the moment they were captured. In doing so, they seem to overwrite their original mistakes, like getting spotted by the Air Force. Which makes the whole subplot of recovering the tapes incredibly stupid and pointless. Why worry about a scratch you got on your car when you’re just going to crash it anyway?
Upon their return to the future present, I can only guess they are shocked to learn that a race of magnanimous elk men now rule over Earth. The butterfly effect is a bitch. With the number of indiscretions Kirk has in a typical episode, it’s amazing the universe even still exists.