The Man Trap - S1-E2
Continuity mistake: Kirk jokes with Bones after they land about flowers and is holding some hay or grass in his hands. After Bones makes the comment about bribing girls, Kirk lowers his hand off screen but with the grass still in it. It jump cuts to a different angle from further away and suddenly his hand is empty, and there is no grass on the ground where he could have dropped it. (00:00:57)
Continuity mistake: When the computer opens and begins operation in Gary Seven's office, it's white. In the close up, it goes from white to purple when asking for identification. Afterwards, the color continues to change.
The Immunity Syndrome - S2-E18
Continuity mistake: At the shuttle craft deck, Spock is standing on the same side of the door as McCoy, then moves to the other side. When McCoy looks at Spock, he is standing on McCoy's side of the door again, then is back on the other side when the door opens.
The Return of the Archons - S1-E22
Continuity mistake: After Kirk and the landing party beam down, they are met by a man who tells them where they can stay for the night but they will have to hurry because it's almost the "red hour." At that time the camera shows a clock that reads 5:58. After being introduced to the daughter of the man who can give them shelter, a gong rings and magically it is 6:00, 2 minutes later, although only 32 seconds of real time has passed. (00:05:18 - 00:05:50)
Continuity mistake: Spock is standing in the background with his back to the wall and his hands behind him. A few seconds later, the shot changes to him deep in the "Plak Tow", with his left shoulder touching the wall and with his hands intertwined. The next shot has him standing with his back against the wall again, hands behind his back again. The scene would have flowed nicely if they hadn't inserted the "Plak Tow" shot in between. That two second clip had been used already a few minutes earlier. (00:33:03)
The Ultimate Computer - S2-E24
Visible crew/equipment: After M-5 fires on the other starships Daystrom speaks to M-5 about the murders, then when Kirk walks over to Daystrom and tells him the M-5 must be destroyed, the shadow of the moving boom mic is visible over Daystrom. The white tape mark is also visible on the floor near Uhura's chair, where McCoy had been standing earlier. (00:42:15)
Continuity mistake: While Kirk, Spock, and McCoy attempt to escape, Merik contacts Enterprise with the stolen communicator and the Proconsul stabs him, then when Merik tosses the communicator it lands in front of Kirk's feet in a closeup. The problem is that in the closeup Kirk is wearing his black uniform pants, but during this scene Kirk is wearing the light colored slave pants. Also interesting to note, when the sword landed on the floor in front of Spock's feet, the Vulcan is wearing black lace-up flat footwear instead of his black uniform boots. (00:46:35)
Continuity mistake: When Scotty, Kirk, and the others follow Spock's signal to the chamber with the Controller, they encounter Kara and she activates their pain bands. Spock's body has a pain band around his waist as the other men drop to the ground, but after McCoy tells Kirk, "Spock, no pain," the pain band is missing from Spock's body, then in the next shot it reappears when he goes after Kara's bracelet. (00:35:05)
Continuity mistake: When Kirk and his landing party beam down to the planet there are six shots of Morg, who have their right arms covered in fur in all those flipped shots, but when Morg attack the landing party it's their left arms covered in fur. Presumably, the first six shots were flipped for direction continuity. (00:13:15)
Revealing mistake: After Scotty finally locates Seven on the gantry while he's tampering with the rocket, it cuts to a quick shot of Kirk and Spock, then in the following shot of Roberta when she turns the vault's combination locks, the stunt wire is visible behind her as it moves up to turn the door's wheel handle. (00:35:25)
The Ultimate Computer - S2-E24
Continuity mistake: During the scene with the ore freighter, there are four closeups of Spock while he's bent over the scope at his station, and in the background behind Spock we can see Kirk and others on the bridge are gone. It also occurs in the earlier scene during the encounter with the two starships. (00:24:00)
Visible crew/equipment: After Melakon shoots at the curtained window and kills John Gill in the broadcast booth, Isak shoots Melakon, then when Eneg stops the soldier who points his gun at Isak, the shadow of the boom mic dips into view at the top, left side of the screen. (00:45:50)
Deliberate mistake: When Rojan asks Kelinda if she wishes to remain with Kirk, she replies that although Kirk is "most interesting" she wishes to go with him, and the next closeup of Rojan is flipped. (00:48:15)
Visible crew/equipment: When Scotty joins Thalassa while she's working, she asks if he has "prepared the megaton hydrocoils," and the shadow of the boom mic can be seen moving at the top of the screen. (00:33:20)
Revealing mistake: During the fight between Kirk and Tracey, the outline of the knee pads under Kirk's pants are visible, particularly while Kirk is on the floor with his knees bent.
Continuity mistake: When Kirk and Mara are in the transporter room for intraship beaming, Kirk is wearing his usual Starfleet boots with heels, but while Kirk and Kang are fighting Kirk is wearing flat bottom boots. (00:43:25)
Visible crew/equipment: After Kirk and Tracey have fought, Sulu and two others beam down armed with phasers, and when Kirk tells Leslie to free McCoy and Spock, two white tape marks are visible on the floor in front of the actors. (00:45:20)
Continuity mistake: When Kirk and McCoy join Spock and Galloway on Exeter's bridge, McCoy kneels down and uses his med tricorder with its strap crossed over his shoulder, but in McCoy's closeup the strap is gone, then next shot the strap is once again over McCoy's shoulder. (00:04:25)
Deliberate mistake: When Spock is brought to the Yang ceremony to join Kirk and McCoy, after Spock responds that although he is weak their "need for departure is even more immediate," the very next closeup of Kirk is a flipped shot. (00:34:15)
Operation -- Annihilate! - S1-E30
Visible crew/equipment: When Kirk and the landing party are standing on the transporter pads ready to beam down to planet, the camera pans to the right as the transporter operator stands at the console, and the end of the set is visible with black cables lying on floor. (00:07:15)
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.