Revealing mistake: When Kirk and Miri are in the kid's hideout, Kirk is attacked by Louise, the wild woman. After Kirk knocks her off his back, she falls to the ground and tries to get up again, Kirk has to resort to stunning her with his phaser. The blue beam starts coming out then starts coming back towards the phaser before going back out again. (00:26:12)
Tomorrow is Yesterday - S1-E20
Revealing mistake: Traveling towards the Sun and away from the Earth, parts of the Enterprise are missing due to superimposing the model into the current shot. As the Enterprise goes by, one of the warp engines seems to be disintegrating at the rear. (00:42:05)
Revealing mistake: As Spock carries the crewman, the second spear hits a rock. As it does, you can see the Styrofoam chips fly up.
Revealing mistake: After being put in the cell, when the camera is in a closeup of Spock, you can see the lines in the prosthetic ears, and can easily tell where the makeup is blended into his real ear.
The Gamesters of Triskelion - S2-E16
Revealing mistake: As the camera does a close up of the Master Thrall, the line of the bald skin cap is visible. (00:05:10)
Revealing mistake: A number of times through the episode, the wire holding Nomad up and moving it around is visible. Example: When Nomad first moves off the transporter pad, look directly above it; the black wire can be seen in front on the light over the pad.
Revealing mistake: As the Romulan ship is tilted, the dust and debris fall straight down, rather than diagonally toward the wall and floor joint.
What Are Little Girls Made Of? - S1-E8
Revealing mistake: When Korby introduces the new android Kirk to Chapel, as the duplicator table slowly turns the edit in the footage can be seen in this shot, just as the real Kirk suddenly vanishes from the space he was in.
Revealing mistake: After Spock finds Gaetano's body he carries him back to the shuttle, and in the interior shot as McCoy and Boma carry Gaetano's body to the back, we can see though the shuttlecraft's doorway the top of the set's blue backdrop.
Revealing mistake: At different points during the Metrons' transmission to the Enterprise, both Kirk and the Gorn pop into the picture a few seconds after the rocky landscape appears. (00:37:00 - 00:37:55)
Revealing mistake: Near the end of the episode, after Kirk has destroyed the orb, we see Korob and Sylvia in their true form. As they move, you can see the black strings used to manipulate the puppets.
Revealing mistake: When Kirk & Spock beam down with Lincoln to the supposedly newly-created non-volcanic landscape, there are footprints all over the ground. They disappear a few shots later, though.
Revealing mistake: When Kirk pushes Plasus against a rock wall in the mine, a huge upper section of the "solid rock" wobbles. (00:43:20)
Requiem for Methuselah - S3-E19
Revealing mistake: When Spock examines the unknown Brahms waltz, we get a close-up of the music. Unfortunately, the hand-written score bears no resemblance whatsoever to the piece Spock has just played, though he expressly identifies it as such. (00:19:10)
Revealing mistake: When Marta kisses Kirk, her hands leave green make-up smeared all over the left shoulder and back of his uniform tunic. (00:22:05)
Let That Be Your Last Battlefield - S3-E15
Revealing mistake: Due to the use of stock footage once again, Sulu's console viewer appears and disappears repeatedly throughout the episode. (00:08:45)
Revealing mistake: When McCoy is examining Charlie in sickbay, several shots of the diagnostic panel show a clear reflection of Charlie's upright profile. But Charlie isn't sitting up during the exam - he's lying flat on the table. The close-ups of the panel were shot while actor Robert Walker Jr. was either sitting or standing nearby. (00:04:10)
Revealing mistake: While Nona is struggling with her Villager attackers, the camera tilts just far enough to show, in the distance, a nice (if slightly smoggy) view of buildings, docks and boats in Santa Monica Harbor. (00:45:00)
Where No Man Has Gone Before - S1-E4
Revealing mistake: When Kirk & Spock are watching Gary read the pages on the monitor one after the other, look closely: it's the same two pages back and forth.
The Man Trap - S1-E2
Revealing mistake: In the corridor, as Sulu touches the face of the dead crewman, the man's eyelids flutter. (00:30:15)
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.