When Tommy looks across the bridge after Kirk leaves, the long shot shows Hadley at the navigational station. However, when Tommy walks over to look at the console, Chekov is in the position.
In one of Prof. Starnes' log entries he says that the civilization on Triacus was destroyed by a "natural catastrophe". Yet later when Spock is asked about them by Kirk, he says they were a "band of marauders" who "made constant war" and that they "were themselves destroyed by those they preyed upon".
When Spock grabs Kirk and they get into the turbolift, it starts up and goes exactly where they want it to go even though they don't give it any verbal commands or use the hand control.
No wonder McCoy doesn't like to use the transporter! Kirk beams down two security guards to the planet - they don't "lock on" to the planet or call up the guards already on the planet to get a lock-on signal, or do any kind of double-checking to see if there are any gravitational anomalies, or anything. Who would want to travel by a transporter when they're that careless?
The stardates of Starnes' entries are 5025.3, 5032.4, and 5038.3 But Kirk gives the stardate of when they arrive at the beginning of the episode as 5029.5, so apparently Starnes made two entries after he died.
Who is taking the picture of Professor Starnes as he records his entry? Presumably he's recording himself using his tricorder...but in the picture he's holding the tricorder.
Unlike in "City on the Edge of Forever", Kirk is able to play back the tricorder's recording...on the tricorder. He doesn't have to give it extra power or hook it up to a computer or anything.
How does Kirk know Gorgan is called Gorgan? The children never call him that, Spock never mentions it in the research. The first time anyone calls him Gorgan is...when Kirk calls him Gorgan.
What happened to the two security guards stuck on the planet? At the end of this episode the Enterprise just flies on to its next assignment.
Don: Parents like stupid things.
Kirk: Most legends have their basis in facts.
Spock: Humans do have an amazing capacity for believing what they choose... and excluding that which is painful.
Spock: Captain, so long as the children are present, there is danger. They are the carriers.
Kirk: Spock, they're not the alien beings. They're children being misled.
Spock: They are followers. Without followers, evil cannot spread.
Kirk: They're children.
Spock: Captain, the 430 men and women on board the Enterprise and the ship itself are endangered by these children.
Kirk: They don't understand the evil that they're doing.
Spock: Perhaps that is true, but the evil that is within them is spreading fast, and unless we can find a way to remove it...
Kirk: We'll have to kill them.
Spock: Evil does seek to maintain power by suppressing the truth.
McCoy: Or by misleading the innocent.
Uhura: ...Captain...I'm old...disease...a slow horrible death...disease captain!
Children: - Bizzy. Bizzy. - Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Guess what we are.
Chapel: I know - a swarm of bees.
Children: Bizzy! Bizzy! Bizzy! Bizzy! Bizzy! Bizzy!
Kirk: Maybe that's what's registering on your tricorder.
Spock: I'm not familiar with anxiety, but I wasn't aware it could be registered on sensors.
Gorgan: I would ask you to join me, but you are gentle, and that is a grave weakness.
Kirk: We're also very strong.
Gorgan: Ah, but your strength is canceled by your gentleness. You are full of goodness. Such as you cannot be changed.
Children: Hail, hail, fire and snow. Call the angel, we will go. Faraway, for to see, Friendly Angel come to me.
Paul Baxley who was the stunt coordinator for this episode is uncredited.