Originally this episode was designed to be the second half of a two-part story, following a cliffhanger ending of 1.4 "The Naked Time" in which they get thrown back in time and don't manage to return to their own time. But the producers decided to split them into two independent stories, thus the somewhat non-sequitur ending of that episode.

I decided to make this an extended reference to I Dream of Jeannie, since this episode really does feel more like an episode of that than an episode of Star Trek. To me, anyway.

Transcript

1
Caption: Patrick Air Force Base, Florida, 1969:
Radar operator: Blip, sir. Looks like a UFO.
Captain: Scramble fighters!
{inset}
Caption: In the sky:
{the Enterprise is flying in the sky}
2
Captain's log, Stardate 3113.2. A black star has sent us plunging through space, out of control.
Uhura: No Starfleet signals, but...
Radio: Cape Kennedy. The first manned Moon shot blasts off Wednesday.
Kirk: Moon shot? That was in 1969. How??
Spock: It's just a jump... to the left...
3
Sulu: Fighter chasing us, sir!
Kirk: Beam the pilot aboard.
Spock: But... time paradoxes...
Kirk: How many rules do I need to break before you realise it always turns out all right?
4
{transporter room}
Kirk: Welcome aboard.
Major Nelson: Uh. Major Tony Nelson, United States Air Force. Serial number 4857932.
Kirk: Relax, we're friends. I'm Captain James T. Kirk. We're from the future.
Major Nelson: You must be... Yeah, okay, I can't talk.
5
{Enterprise corridor}
Major Nelson: Female crew?
Kirk: Oh yes. We're very socially progressive in the 23rd century.
Major Nelson: What do they do?
Kirk: Make coffee, hand me reports to sign. One is even a nurse!
6
{bridge}
Spock: We must return him. His yet-to-be-born son commands the first Saturn mission.
Kirk: Okay, we return him.
Spock: We can't return him. He knows too much about the future.
Kirk: You should be solving problems, Spock! What do we pay you for?
Major Nelson: Son?
7
Major Nelson: I'll help you recover the radio tapes and film of your ship in a slapstick infiltration of the Air Force Base.
Kirk: You have experience with this sort of thing, Major Nelson?
Major Nelson: Oh, you have no idea.
8
{Patrick Air Force Base}
Sulu: Here are the data tapes.
Kirk: Look at these old computers.
Sulu: Yeah. So glad we use Zip disks in the future.
9
Caption: Kirk is captured!
Dr Bellows: I'm Dr Bellows, base psychiatrist. Who are you?
Kirk: James T. Kirk. I'm from the future.
Dr Bellows: I suppose you came back naked?
Kirk: Er... no.
Dr Bellows: Darn.
10
Dr Bellows: Something fishy is always going on at this base, Kirk, and I'm going to get to the bottom of it!
Major Healey: Dr Bellows!
Dr Bellows: What is it, Major Healey?
Major Healey: Tony's vanished from his plane!
11
Major Nelson: Here I am. With an alien from the future.
Dr Bellows: A likely story!
Major Nelson: Uh... and a magic genie.
Dr Bellows: What next?! A flying nun? A talking horse? A blended family with three girls and three boys?!
12
Jeannie: I'll blink and send you back to the future by genie magic.
Kirk: That's silly!
Spock: It has a better chance of working than my cockamamie "slingshot around the sun" idea.
SFX: BLINK!