Tomorrow is Yesterday - S1-E20
Revealing mistake: As the camera looks at the pilot in the cockpit, there are supports on either side of and behind him as well as no clouds where there should be, showing he is on a sound stage set.
What Are Little Girls Made Of? - S1-E8
Revealing mistake: As the big android holds Kirk up by the wall, you can see the skin wig worn by the actor wrinkle up.
Requiem for Methuselah - S3-E19
Revealing mistake: As Kirk pulls the shroud away from the Rayna duplicate, look closely at the part of her head just below her left ear. The bald cap she wore to conceal her hair and give her an unfinished look.
A Taste of Armageddon - S1-E24
Revealing mistake: It is easy to tell where the matte painting and live action area meet when Fox and the assistant appear.
Revealing mistake: While Kirk watches, the machine fires at the Enterprise. As Spock is knocked backwards, watch his hands as he goes forward. They automatically go into a certain, almost practiced position. Then a moment later, the Communications officer is reporting to Spock. As she does, another shot hits the ship. She and just about all the crew react to the jolt a second before the camera and lighting crews simulate the hit. (00:26:40)
Revealing mistake: Accounting for some effects being re-done by modern digital formatting, when the Enterprise approaches the drifting Constellation, as it rotates, you can see a star pass through the solid part of the Constellation's saucer.
Let That Be Your Last Battlefield - S3-E15
Revealing mistake: After Kirk shuts down the self destruct, he asks Spock if the ship is heading for Arianas. At one point in the dialog, you can see the display for the self destruct sequence is still on the screen, just not lit up.
Let That Be Your Last Battlefield - S3-E15
Revealing mistake: When the camera is close up on Beal's face, you can see a bit of real flesh color where the black and the white greasepaint used didn't quite match up.
Revealing mistake: In the tent after Kirk and friends give up their weapons, there is a small fire in the holder in the center of the room. Although the flames are slightly off center to the camera's left, the are projections of flame light from off the camera's right offscreen.
Revealing mistake: When the delegation of locals approach Kirk's party, the Red-shirt yells "KLINGON!" and goes to fire. As he moves, you can see the outline of the block the alien weapon will stick in.
Revealing mistake: About 4/5 through the show, while the Vulcan is being killed, if you look at Lincoln's wrist, you can see his makeup line.
Revealing mistake: The shot of the castle on Rigel VII seems to be what Pike sees through his eyes, but in the next shot he himself is in the shot.
Revealing mistake: When Kirk, Spock and McCoy study a diagram that shows various parts of the Nomad probe, the lower right of the diagram reads "Computer Data Banks Recall & Transmition". It should read "Transmission".
Revealing mistake: McCoy is knelt down with the rather comically named Flavious Maximus attacking him. On the remastered version it is obvious it is a stunt double doing the part. (00:34:20)
Revealing mistake: Kirk jumps across the burning hot forge to hide from the people approaching him, only problem is that he actually touches the red hot coals with the palm of his hand. Somehow he managed to avoid serious burns. (00:31:15)
Revealing mistake: As Scotty is cutting through the wall, the line where the burn is supposed to go is outlined on the inside of the wall.
Revealing mistake: It would seem that with the incredible advanced knowledge and furnishings that have been bestowed upon the Imorg down below, the 'Teacher' should have at least provided them with adequate high tech structuring and not the ratty, torn and warped substandard sheet rock seen on the bottom of the walls in these two camera shots. Yep, they can remove and restore a brain but can't find a place to buy good quality plasterboard. (00:23:40 - 00:33:51)
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.
Revealing mistake: When the Talosians place Christopher Pike and Vina into the "picnic" illusion (in the countryside on Earth), Pike wanders around marveling at how real it all seems. Well, "real" except for the fact that Pike's body is casting 4 distinct shadows in 4 different directions on the ground, the result of studio set lighting.
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.