Most of the outdoor scenes were done with voice-overs due to too much background noise during filming, but the voice-overs at the beginning of the epiosde on the surface of the planet are very obvious and poorly done. Budget restrictions, no doubt.
It seems odd that McCoy isn't able to help Miramanee after she gets hurt by some flying rocks. They were able to save Spock when he got shot in "A Private Little War," he saved Kirk when he got stabbed in "Journey to Babel" and modern medicine even saved Capt. Pike, who was mutilated from radiation. However, with all their advanced medical abilities they can't stop some internal bleeding from getting hit with rocks.
When Miramanee takes the medicine badge off of Salish and puts in on Kirk, take note of the space age elastic band that the badge is tied to.
Unavoidable, but Kirk uses good old-fashioned 60s mouth-to-mouth rather than subsequently developed CPR technique to revive the boy.
When Kirk heads for the monolith as the storm whips up, in some shots the sky is a clear blue and the nearby lake's surface is perfectly calm.
When Kirk and Miramanee are sitting on the ground and she is telling him that she is pregnant, a fly steals the scene by landing on Shatner's forehead and remaining there for several seconds.
Since the warp drive is out, and Scotty claims he can't repair it in space, how are they ever going to get back to a starbase at impulse speed? If the nearest base is four light years away, it's going to take them four years. It takes them two months just to get back to the planet. Presumably they're going to send out a distress call and get a tow, but then why doesn't the tow ship show up in the two months it takes them to get to the planet?
The idea that Starfleet goes around preventing natural disaster on unaffiliated planets whose people don't know of the Federation seems a little odd - at the very least it would seem to be a violation of the Prime Directive (at least as they explain it later in Next Generation episodes like "Pen Pals").
When Spock orders the phasers to fire, they shoot outward from the ship at an angle from each other, but when they hit the asteroid they converge at a single point.
Once its power circuits burn out and the phasers are useless, why doesn't Spock try and use the photon torpedos?
McCoy: What's the matter, Jim?
Kirk: What? Oh, nothing. Just so peaceful, uncomplicated. No problems, no command decisions. Just living.
McCoy: Typical human reaction to an idyllic natural setting. In the twentieth century, we referred to it as the Tahiti Syndrome. It's particularly common to over pressured leader types, like starship captains.
Kirk: Ah, Tahiti Syndrome.
Spock: I want full power, Mr. Scott.
Scotty: Aye, sir. All right, you lovelies. Hold together.
Kirk: Miramanee... tell me about the wise ones.
Miramanee: Tell? But a god knows everything.
Kirk: Not this one. Tell me.
Kirk: I need time to remember.
Miramanee: Here there is much time. For everything.
Spock: Lock all phasers on that mark. Maximum intensity, narrow beam. I want to split that fissure wide open.
McCoy: You sound like you're cutting a diamond.
Spock: Very astute, Doctor.
Scotty: That Vulcan won't be satisfied until these panels are a puddle of lead!
Scotty: My bairns. My poor bairns.
Miramanee: Tribal law betroths me to our leader. If there is another, I will step aside.
Kirk: No, Miramanee, there's no one else, in my mind or my heart.
Miramanee: God's wish is above tribal law.
Kirk: Name the joining day.
Miramanee: The sooner our happiness together begins, the longer it will last.
McCoy: Well, Spock, you took your calculated risk in your calculated Vulcan way, and you lost--you lost for us, you lost for that planet, and you lost for Jim.
McCoy: Back to that planet? Without warp speed, it'll take months.
Spock: Exactly 59.223 days, Doctor, and that asteroid will be four hours behind us all the way.
McCoy: Well, then what's the use? We might not be able to save the captain even if he still is alive. We might not be able to save anything, including this ship! You haven't heard a word I've said. All you've been doing is staring at that blasted obelisk.
Spock: Another calculated Vulcan risk, Doctor.
Salish: You bleed. You bleed, Kirok. Behold a god who bleeds!
Spock: I'm not hungry, Doctor. And under stress, we Vulcans can do without sleep for weeks.
McCoy: Well, your Vulcan metabolism is so low it can hardly be measured, and as for the pressure, that green ice water you call blood...
Spock: My physical condition is not important, Doctor. That obelisk is.
McCoy: Well, my diagnosis is exhaustion brought on from overwork and guilt. You're blaming yourself for crippling this ship Just as we blamed you. Well, we were wrong. So were you. You made a command decision. Jim would have done the same.
Kirk: Miramanee. Come here. Miramanee.
Miramanee: Each time your arms hold me is as joyous as the first.
Spock: (about Kirk) His mind--he is... an extremely dynamic individual.
Kirk: More symbols. Can you read them?
Spock: I do have an excellent eye for musical notes, Captain. They would seem to indicate that this series of relays activated in their proper...
Kirk: Spock, just press the right button.
Miramanee: When I am better... it will be as it was, will it... not?
Kirk: If that's what you want.
Miramanee: We will live long and happy lives. I will bear you many strong sons. I love you always.
Kirk: And I love you, Miramanee... always.
Miramanee: Each kiss... is as the first.
Miramanee's pregnancy is considered by many Star Trek fans to be the only incontrovertible evidence that Captain Kirk had sexual relations with an alien or human female during the time frame of the original series.