Dr. Janet Wallace: You know, you never asked me why I got married after we called it off.
Kirk: Well, I supposed that you met someone you loved. I met a man I admired. A great man.
Kirk: And in your field. You didn't give up a thing.
Dr. Janet Wallace: No. Just you.
Kirk: Bones, I believe you're getting gray!
McCoy: Well you take over my job and see what it does to you!
McCoy: I don't know what's causing it. A virus, a bacteria, or evil spirits. I'm trying to find out.
McCoy: Go down to your quarters and get some sleep.
Lt. Arlene Galway: No. I don't want to sleep. Can't you understand? If I sleep, what will I find when I wake up?
Chekov: "Give us some more blood, Chekov. The needle won't hurt, Chekov. Take off your shirt, Chekov. Roll over, Chekov, breathe deeply, Chekov! Blood samples, Chekov; marrow samples, Chekov; skin samples, Chekov." If, If, I live long enough, I'm going to run out of samples.
Sulu: You'll live.
Chekov: Oh yes I'll live, but I won't enjoy it.
Kirk: Look at me. What do you see?
Dr. Janet Wallace: I see Captain James Kirk, a man of morality, decency, handsome, and strong.
Kirk: And old, and rapidly growing older.
Dr. Janet Wallace: Jim, please.
Kirk: What are you offering me, Jan? Love, or a going-away present?
Spock: I have a question for the doctor. Doctor, the ship's temperature is increasingly uncomfortable for me. I've adjusted the environment in my quarters to 125 degrees, which is at least tolerable. However, I...
McCoy: Well, I see I won't be making any house calls on you!
Spock: I wondered if perhaps there was something which could lower my sensitivity to cold.
McCoy: I'm not a magician, Spock, just an old country doctor!
Spock: Yes, as I've always suspected.
Spock: Doctor, you heard the computer's analysis of Captain Kirk's physical age. Do you agree with it?
McCoy: It's a blasted machine, Spock! You can't argue with a machine.
McCoy: Don't just stand there jawing, Spock. You and Dr. Wallace get cracking!
Commodore George Stocker: Lieutenant Uhura, let me know if we contact any Romulans.
(weapon fire shakes the ship)
Uhura: I think we just made contact, sir.
Commodore George Stocker: Keep trying to raise the Romulans.
Uhura: I'm trying, Commodore.
Commodore George Stocker: If I could talk to them, explain to them why we violated the Neutral Zone.
Uhura: The Romulans are notorious for not listening to explanations.
Commodore George Stocker: Captain I just wanted you to know I did what I thought was best.
Kirk: Noted. You should know, however, that there are very few things a Starbase can do that a starship can't.
Commodore George Stocker: If I may say so, Captain, I am now quite aware of what a starship can do--with the right man at the helm.
McCoy: Because of your Vulcan metabolism, I've prepared an extremely potent shot. However you'll be pleased to know I have removed all the breakables from sickbay.
Spock: That is very considerate of you, Doctor.
Kirk: Well, gentlemen, all and all, an experience we'll remember in our old age... which won't be for some while, I hope. Take over, Mr. Sulu. Steady as she goes.
Sulu: Steady as she goes, Captain.
Kirk: I thought I said that.
When the Romulans fire their weapons at the Enterprise, they start out as the typical plasma beam but then the producers cut to a reused shot of photon torpedoes hitting the Enterprise. This is corrected in the re-mastered version.
At the time of the episode, the affected crew range from early twenties to late forties or early fifties. McCoy states they are aging at the rate of thirty years to the day, and Spock estimates they have "less than a week" to live. In fact, they'd have about three days, perhaps a little longer for Spock - and that assumes medicine has managed a hundred year typical lifespan by the 23rd century. While three days is certainly "less than a week" Spock is usually far more precise. In addition, Spock claims their mental faculties were atrophying at a far faster rate, and that they would be entirely senile "long before" that point. At one time, doctors generally accepted that people became senile as they aged; medicine now realizes this is actually a pathology (Alzheimer's disease and a handful of similar and much rarer conditions) and not an inevitability.
The "crude" adrenaline-based radiation treatment not only stops the aging, but cures all the physiological damage caused by the radiation. The victims' hair goes back to normal, their lost memory cells regenerate, their skin smooths out, etc.
The Gamma Hydra IV facility is initially referred to as an scientific expedition, but then is later described as an "experimental colony." It's not clear what is experimental about the colony, but as shown in other episodes such as "This Side of Paradise," it's clear that a colony has to have a much larger population to maintain a viable population.
For the remastered version with premade studio syndication cuts, the scene of Galway's death is removed. Viewers are left to wonder what happened to her at the end since McCoy makes no mention of her needing a cure.
Recycled footage from "Journey to Babel" of Chekov and Sulu is used for the last scene of them on the bridge. This leads to a continuity gaffe as Walter Koenig is wearing the much larger wig he sported in the early season episodes.