Other mistake: As Kirk and party duel against the Klingons, there's a heavy-looking round conduit on the wall right before the turbolift door that gets knocked down so it stands as a big flower pot. A moment later, it's back in position.
Continuity mistake: The first time we see the ship travelling at Warp Nine, it is moving in a level, straight path. Next time, the rear end is elevated above the line of flight. The next time, it's moving in level flight again.
Audio problem: The bartender comes over and brings whiskey and five glasses, but we hear six glasses hit the table.
Revealing mistake: During the televised fight, in the wide angle shots, you can tell it's Spock's stunt double fighting.
The Empath - S3-E12
Revealing mistake: When the Vian fires his weapon at Kirk after the crew finds Gem, Kirk flies backwards. At this point, Kirk is not William Shatner but a stunt double.
Continuity mistake: As Gary Seven starts to talk to the computer, it has a light gray exterior. When it first talks, the trim turns purple, then it's back to light gray.
Character mistake: When Kirk turns to face Spock and McCoy to introduce them to Sarek, the hangar deck nameplate on the wall is misspelled. It reads "hanger deck".
The City on the Edge of Forever - S1-E29
Continuity mistake: When trying to catch McCoy, Kirk's pants get dirtied. After coming out of the Guardian's time portal in the Depression, his pants are clean.
Character mistake: Mr Seven calls the security guard "Sergeant" but he is a corporal.
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.
Character mistake: When Kor describes the effects of the mind-sifter to Kirk (who is still in disguise as an Organian), he says the machine would leave him "more vegetable than human." There is no reason a Klingon would reference humans while speaking to a person he believed to be Organian.
A Piece of the Action - S2-E17
Revealing mistake: The drawers of Krako's desk are on the front side, not on Krako's side where they should be.
The City on the Edge of Forever - S1-E29
Factual error: Spock picks a lock during the great depression, but the lock is from the late 50's.
Continuity mistake: The second time McCoy is shown in the Sickbay, he is first shown sitting and writing. A moment later, he's standing bent over the terminal.
The Return of the Archons - S1-E22
Audio problem: In the transporter room, as Kirk is talking to Sulu, the door opens, McCoy comes in, and the door shuts. Trouble is that the characteristic sound of the door is missing.
Continuity mistake: In the finale of the fight between Kirk and Finney, Kirk's shirt is torn, exposing his right shoulder and arm. As Kirk (the stunt double) goes for the knock out blow, the shirt is only a little torn in the front. Then the close up on Kirk catching Finney, his shoulder is exposed again.
Continuity mistake: In the dining hall, Korab leans over to listen to his cat. As he does, his right hand is at seat level. A second later, his right hand is up by his shoulder. (00:22:20)
Continuity mistake: In most shots, the Constellation's impulse engines are lit up orange, but when moving to meet the Enterprise, they're not lit up, though the ship is moving.
Continuity mistake: Spock nears the command chair, where a seated Decker is leaning on the left armrest. A second later he is leaning to the right.
