Continuity mistake: In a wide shot of the Capellons and the Klingon walking down the hill, the Klingon trips and falls to the ground and picks himself up. Next shot, tight group with Klingon, he is suddenly brushing off his pants.
Suggested correction: After Kras falls, the next shot you see him still on the ground and starting to stand up, although Maab blocks the view of him. The shot cuts to the rocks and then when it cuts back, you see Kras walk up and stand next to Maab, then he starts to dust himself off.
Suggested correction: Why would he not be doing that in the next shot? There is no continuity issue.
Visible crew/equipment: The action is shifting back and forth from the bridge where the alien ship is attacking and sickbay where McCoy is operating on Sarek. In two separate takes when the scene shifts to sickbay McCoy is standing at the operating table. I noticed a wisp of smoke rising from McCoy's right side (left side of screen). It appears to be from a cigarette in an ash tray below camera level either beside McCoy or near the head of Spock's bed.
Suggested correction: This was an intended physical effect to simulate the cryogenic surgery that McCoy was performing on Sarek.
Stupidity: When Gary 7 learns that agents 201 and 347 were killed in an automobile accident, he must take over the mission and save the earth from nuclear war. However, their technology allows them to transport anywhere they want through the vault device. It makes no sense for both agents to drive to McKinley Rocket Base when they could have easily transported there.
Suggested correction: Good point, but it seems more likely that 201 and 347 were executing a careful plan that depended on their cover as normal humans acting normally. Using transporter technology risks discovery. Gary Seven only used the vault transporter as an emergency measure, missed being observed materializing by mere seconds, and was detected by a guard moments later. Same for Kirk and Spock.
The Immunity Syndrome - S2-E18
Other mistake: When the probe emits a loud high-pitched tone, everyone is in pain, with the exception of Mr. Spock, who is supposed to have super sensitive hearing.
Suggested correction: Spock has also been shown to be able to control his own pain.
Factual error: Kirk, McCoy, and Spock are chained to the dungeon wall, with McCoy noticing he is next to a skeleton, also chained. This is incorrect, as a skeleton's bones are held together by cartilage, which would rot over time. Therefore, the skeleton would not be hanging intact, but would be a pile of bones on the floor.
Suggested correction: As we learn in the episode, the 2 aliens created the entire castle only recently to appeal to the human's primal fears and superstitions. A pile of bones on the floor would not have the frightening impact of a hanging skeleton.
Plot hole: Commodore Decker takes over command of the enterprise but Spock says if McCoy can certify him incompetent (which he obviously is) he can be relieved of command. McCoy says he will certify him now, so why doesn't he? In other episodes it has been stated that McCoy can order anybody regardless of rank to an examination to see if they are physically or mentally fit.
Plot hole: How did the android Norman get aboard the enterprise? If he beamed aboard I'm sure someone would have noticed and where did he beam from? The Enterprise was nowhere near any planet and I'm sure they would have detected any spacecraft nearby.
Suggested correction: These are unanswered questions, not plot holes.
But something phrased as a question because it has no decent answer can constitute a plot hole.
Character mistake: Kirk is surprised by Spock's behavior, but shouldn't everything about Spock be in his records? Kirk should therefore know about Spock's needs and have planned for them.
