The mechanics of the portal are unclear. Kirk, Spock, and McCoy are able to communicate across two different time eras, suggesting that the portal is open to both eras simultaneously. There's no reason for that to be the case, and it seem unworkable: if the portal is open to both eras simultaneously, where would something going through end up? What if people entered their portals from two different eras simultaneously? Also, both portals remain open at least long enough for Kirk to find his way back. This may mean Atoz left them open once the landing party realized they needed to be "prepared" and come back to do so. However, he's not there when Kirk returns, waiting to prepare him. What else does Atoz have to do?
Since Atoz knows that the landing party is unprepared, it's not clear why he doesn't call out and help them find their portals so they can come back and be prepared. He has no reason to believe that they want to do anything else, and until the very end seems to think they're natives.
Atoz seems deliberately difficult. The disc that McCoy watched was one of only two that were being used. McCoy left it in the viewer. Even if he put it away for some reason, how hard can it be for him to remember where he put it? Instead he and Kirk spend time going through every disc relating to the era.
Atoz tries to push Kirk into the portal and send him to another time. However, as established earlier if a time traveller isn't prepared then they'll die. It's also established that if a time traveller is prepared for a historical era, they can't survive in the present. Since Atoz is trying to save Kirk's life, he must have used the Atavachron to "prepare" the captain for whatever era he's sending him too. But... there's no indication and no time available where Atoz can or does unprepare the captain so he can survive in the present.
It's not clear why the Enterprise visits Sarpeidon. The Prime Directive would presumably keep them from interfering, and even if it wouldn't they don't have the resources to evacuate an entire planet, much less in the three hours between when they arrive and when the sun goes nova. Apparently they're there just to see why everyone disappeared... three hours before the population would have disappeared for good anyway. And then turn around and do nothing if they do find any survivors.
Atoz specifically says that he "personally" sent everyone on the planet through the portal. While no specific population is stated, Sarpeidon appears to be a burgeoning civilization, with advanced technology and at least one era with an equally well-developed and populated society, as well as one dictatorship that felt comfortable banishing whole families into the past. The facility shown, with its relatively small area and limited viewing capability, couldn't possibly handle so large a population in the relatively short period suggested given the Federation's knowledge of the nova and awareness of a civilization on the planet.
When first the Atoz replica and then another replica, and then Atoz himself appear, the men don't appear surprised. However, when they arrived Spock informed them he detected no sapient life forms. He apologizes a few minutes later for "miscalculating" but nobody notices his error at the time or finds it at all surprising that he managed to miss someone. There also appears to be no reason for the real Atoz to not show up on sensors, either from the ship or when the landing party first arrives inside the same building.
Kirk travels back through time only shortly before Spock and McCoy do. However, when he prepares to return to the library he starts to feel the lethal effects of non-prepared time travel. However, Spock and in particular the ailing McCoy are displaced in time for a much longer period and display no physical illness.
Zarabeth's plan doesn't make much sense, as she certainly knows that anyone who goes back without preparation will die. And yet she deceives Spock into staying with her... just so he can die and she'll be alone again.
Spock says he intends to build a greenhouse in the cave in the ice age. However, there wouldn't be any seeds or other source of plant material to grow.
While in his jail cell, Kirk makes a log entry without moving his lips.
The atavachron is identical to the Beta 5 computer in "Assignment: Earth".
When McCoy walks into Zarabeth's outer chamber, he speaks but his lips do not move.
When Spock and McCoy return from the ice age, they're wearing heavy furs. When they reach the other side of the portal, the furs are gone.
Zarabeth's cave walls are rough and unfinished, but the floors are completely smooth and level.
When the prosecutor visits Kirk in his cell a second time, between instantaneous camera cuts, Kirk's hands jump back and forth on the cell bars - sometimes he's holding adjacent bars, sometimes there are bars between the ones he's holding.
Zarabeth has remarkably well-styled hair considering she hangs out by herself in a primitive cave with minimal tools. She dresses quite well and even has flip curls.
Spock tells Zarabeth he came from a world "millions of light-years away." The galaxy is only about 100,000 light-years across--the area the Federation has explored even smaller.
Kirk's arresting officer claims he heard Kirk call out to "Bones." The officer wasn't there when Kirk called out to McCoy at the wall on the transport spot.
Zarabeth: But your friend--he is ill.
Spock: That is true. If I leave him, he may never regain the ship. He would be marooned in this time period. But he is no longer in danger of death, so my primary duty to him has been discharged. And if I remain here, no one of our party would be able to aid Captain Kirk.
Zarabeth: Oh, you make it sound like an equation.
Spock: It should be an equation! I should be able to resolve this problem logically.
McCoy: Zarabeth, you are a beautiful cook. Have you ever been told that?
Zarabeth: Not recently.
McCoy: Oh, well, you'll find Spock is quite delinquent in those matters.
Zarabeth: I hadn't noticed it.
Spock: Dr. McCoy is making excellent progress.
McCoy: Mr. Spock has been practicing medicine without a license. Don't let him doctor you. I'm the doctor around here.
Spock: And known as the worst patient in the entire crew of the Enterprise.
McCoy: You listen to me, you pointed-eared Vulcan.
Spock: I don't like that. I don't think I ever did, and now I'm sure.
McCoy: What's happening to you, Spock?
Spock: Nothing that shouldn't have happened long ago.
McCoy: Are you trying to kill me, Spock? Is that what you really want? Think. What are you feeling? Rage? Jealousy? Have you ever had those feelings before?
Spock: This is impossible. Impossible. I am a Vulcan.
McCoy: he Vulcan you knew won't exist for another 5,000 years. Think, man. What's happening on your planet right now, at this very moment?
Spock: My ancestors are barbarians, warlike barbarians. Who nearly killed themselves off with their own passions.
McCoy: Spock, you're reverting into your ancestors... 5,000 years before you were born!
Spock: I've lost myself. I do not know who I am.
Kirk: You'd better come back with me to the library. Dr. McCoy can see to those bruises.
Woman: (flirtatiously) I'm game, luv. Lead n' I'll follow. Where's "library?"
Kirk: (calling to Spock and McCoy through the Time Portal) Are you still in the library?
Spock: Indeed not! We are in a wilderness of Arctic characteristics!
McCoy: He means it's cold!
Spock: There is no further need to observe me, Doctor. As you can see I have returned to the present in every sense.
McCoy: But it did happen, Spock.
Spock: Yes. But that was 5,000 years ago, and she is dead and buried.
Fop #1: (to Kirk) Down when you're bidden, slave! (after being pushed to the ground by Kirk) You need a lesson in how to use your betters! Who's your master?
Kirk: I'm a free man, sir.
Fop #1: Then you want better manners, free man!
Officer: I heard the spirit talk to him. He answered and did call it 'Bones'.
Mr. Atoz: A library serves no purpose unless someone is using it.
Zarabeth: Do you know what it's like alone, really alone? Weapons, shelter, food... everything I needed to live... except companionship... to send me here alone... if that is not death, what is?
Prosecutor: There are witches! There are!
Woman: Witch! Witch! Witch! They'll burn ya!
Popular Star Trek novelist A.C. Crispin published two books (Yesterday's Son and its sequel Time for Yesterday) as part of her Yesterday Saga, based on the original series episode "All Our Yesterdays".
The base of the viewer that is nearest the the time portal is a re-used prop from "Return to Tomorrow".
The working title for this episode was "A Handful Of Dust".
The interior of the ship is never seen during this episode. Only Scotty's voice is heard.
The librarian Mr. Atoz takes his name from the expression "A to Z"