Visible crew/equipment: When Vaal is not fed and he starts spewing smoke everywhere, you can see a volcano type firework going off just inside his mouth. (00:43:55)
Continuity mistake: In the original version, the planet is the same as the one used in "Bread and Circuses", but when the Enterprise leaves orbit at the end, it is a totally different planet, as it is the one used in "Friday's Child".
Revealing mistake: After Kirk and party are captured by the police, a montage of scenes depicting the planet's buildings plays while the log entry is heard. One of the buildings shown, though hard to read, has the title "Massachusetts Institute of Technology" (M.I.T.) above the columns.
The Immunity Syndrome - S2-E18
Other mistake: As McCoy stands by the hangar deck doors, the plaque over the pressure controls has "hangar" misspelled. It says "hanger".
Other mistake: When Norman goes to the second panel in Auxiliary Control, there is clicking when he turns his right hand, but there is no knob, just a blinking light.
Other mistake: When the Planet Killer hits the Enterprise, the ship lurches 45° to starboard, and the crew fall accordingly. However, the chairs, except for the communications station, stay in place.
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.
The Gamesters of Triskelion - S2-E16
Revealing mistake: When the camera goes in on a close up of the phaser, when the trigger is pulled, the indicator light to signal a reaction by the intended target that's usually too small to be seen or hidden by animation is visible.
Revealing mistake: As Kirk and company exit through the tunnel, the seams of the wall sections are visible.
Continuity mistake: As there were two screen used models of the Enterprise, when the ship is seen flipping from one universe to the other and back, the nacelles of the Imperial Enterprise have the solid red fronts with what appear to be antennae.
Revealing mistake: When Kirk and Garrovick are fighting at the end, Kirk knocks him down. As he helps him up, Garrovick leans against a huge boulder and the papier-mache rock moves very noticeably.
Character mistake: Spock expresses amazement that the natives of this planet speak Earth English, however, he and Kirk were both on the bridge when Uhura tapped into the planet's news broadcast and already know that they speak Earth English, and there's no reason to tell McCoy, because he heard it too. Commenting on it would be illogical. (00:07:00)
The Ultimate Computer - S2-E24
Continuity mistake: The doctor and Spock are facing each other, the camera angle changes and they are suddenly shoulder to shoulder. (00:26:50)
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.
Continuity mistake: After their life threatening surgery, Spock and Sarek somehow manage to switch beds between being in surgery and recovering. (00:45:00)
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.