Continuity mistake: When Scotty thwarts Garth, disguised as Kirk, attempts to beam to the Enterprise using the Queen-to-Queen level three code, Kirk throws a tantrum and accidentally loosens one of his controls during his rant right before he turns back to Garth.
Suggested correction: How is that a mistake?
Continuity mistake: When the Enterprise tries to escape Gothos, and the planet blocks the ship's path each time, Gothos is very transparent, where the stars could be seen through the planet.
Continuity mistake: After Spock nerve pinches Chekov when he goes mad and he is taken to Sickbay, the Tholian ship appears and hails the Enterprise. When Spock says "on main viewer," the shot of Loskene is on the screen, but the back of Chekov's head can be seen when it should be in Sickbay.
The Alternative Factor - S1-E28
Other mistake: When Spock calls Kirk to the bridge after he discovers the Lazarus energy source, he and Lazarus head to the bridge. There is a shot of McCoy standing in the corridor, and one of the red alert panels is burned out while the other is still flashing.
A Taste of Armageddon - S1-E24
Continuity mistake: At the end of the teaser, Kirk orders Yellow Alert, but the Red Alert alarm sounds.
Is There in Truth No Beauty? - S3-E5
Visible crew/equipment: Spock and Dr. Jones carry Koldos into his quarters, and when Spock walks over to the wall communicator to contact the bridge, the camera casts a shadow on the wall as it moves closer to Spock. (00:05:20)
Is There in Truth No Beauty? - S3-E5
Visible crew/equipment: At the dinner, when Miranda stands up to leave, there's a visible white tape mark on the floor near her feet. Then, when McCoy makes his exit Kirk reaches for the rose, and there's a better view of the white tape mark under the table. (00:11:50 - 00:13:45)
Continuity mistake: After the heavy door lands on Korob, his right arm is straight down by his side. The next shot of Korob shows his right arm extended away from his body.
Other mistake: In the Briefing Room, while Kirk is feeling the effects of the disease, Spock tells Scotty that he will call the restart formula in from the bridge. But just a moment later, Kirk enters the Bridge, and Spock is in the Engine Room working on the settings and formula with Scotty.
Audio problem: About a minute or two into the episode, Captain Kirk says "That's incredible" but his mouth doesn't match the words.
The Conscience of the King - S1-E14
Revealing mistake: As Kirk and Lenore leave the cocktail party to walk around outside, they stop to talk. From Kirk's perspective, he is to the left of Lenore, enough to see what should be in view ahead of him. Only seconds later when she leans in to kiss him does he notice Dr. Leighton lying next to some rocks. She was not obscuring his view before. Why didn't Kirk see this while they first started talking? (00:10:36)
Shore Leave - S1-E16
Revealing mistake: After Rodriguez and Angela run from the strafing plane, they end up stopping next to a tree. Angela falls to the ground without Rodriguez knowing that she was hit by the gunfire. He continues to watch the plane disappear with his head looking upwards. When his head comes back down, rather than looking towards her to talk (where her face would be if she was standing), his eyes immediately look down at her on the ground...as if he'd been expecting that she'd be lying there all along. (00:34:01)
Audio problem: Spock uses the intercom to call Mr. Scott who is in engineering. As the shot cuts to a side view of Scotty standing at the controls, he answers "Scott here" but his mouth or lips never move. (00:44:24)
Other mistake: Kirk orders the helm to get phasers ready to fire at the Romulan vessel. When the helm responds, it's not the phaser banks that fire, but photon torpedoes. (00:32:58)
Continuity mistake: After the battle ends, Kirk looks up to the exact spot where the Metron will be standing, way before the Metron even materializes. (00:45:53)
Continuity mistake: After Kirk tells the Metrons that he won't kill the Gorn, he yells out "you'll have to get your entertainment someplace else." Two seconds later, Kirk turns his head to the side and looks stunned. That look of surprise takes place a full second before the Gorn starts to disappear. (00:45:47)
Continuity mistake: In the turbolift, Chekov is standing to the left, but when the door opens he has moved to the right and exits behind Spock. (00:10:40)
Continuity mistake: On the planet surface, in the scene where the three security men walk around the rock, Garrovick has his arm up with his phaser. When the camera angle cuts to him alone, his arm is suddenly down.