The Trouble With Tribbles - S2-E15
Continuity mistake: Kirk is holding three large tribbles while talking to Uhura on the bridge. After McCoy enters, the tribbles keep changing positions in Kirk's hands as the shots cut back and forth. (One on top and two underneath, then two on top, etc.). (00:31:45)
The Trouble With Tribbles - S2-E15
Continuity mistake: When Kirk is standing in the huge pile of tribbles, he's cradling two large tribbles in his arms in full shots, but only one, and in a different position, in close-ups. (00:40:00)
The Trouble With Tribbles - S2-E15
Continuity mistake: The tribble-inundated Kirk is holding one of the small fur balls in both hands in some shots, but when the camera angle changes, that tribble vanishes and his hands are no longer even close together. (00:40:40)
The Trouble With Tribbles - S2-E15
Continuity mistake: Towards the end of the episode when the Enterprise is moving leaving from the starbase, the ship is at an angle to the camera pointing to the right of the screen. The starbase behind it gets smaller and goes up a little. If the Enterprise were leaving the starbase at that angle, the starbase should have moved to the left and then completely off the screen.
The Trouble With Tribbles - S2-E15
Continuity mistake: Mr. Leslie appears as one of the guards in the space station, Stardate 45XX.X. Unfortunately, he was killed in 'Obsession,' Stardate 36XX.X. External websites have a variety of excuses for this miraculous reappearance, but he very definitely dies in the show, with no canonical reason for him reappearing beyond it being a mistake.
The Trouble With Tribbles - S2-E15
Continuity mistake: During the scene when the Klingon agent is exposed by the Tribbles, Kirk first holds the two furballs as if they had a handle on the underside (probably for the parts to make them wriggle). As he turns to Spock (the wide-angle shot), he holds the Tribbles cupped in his hands, his thumbs supporting their flanks. But as Kirk approaches Spock (close-up), he has them 'by the handle' again.
The Trouble With Tribbles - S2-E15
Continuity mistake: When Kirk and McCoy dispute about the tribbles on the Enterprise bridge, Kirk holds the two tribbles in his hands at alternate heights. In the shots where McCoy's face is seen, he holds them next under his chins, but when Kirk's face is seen, he holds them at chest level.
The Trouble With Tribbles - S2-E15
Continuity mistake: After Kirk opens the bin, the Tribbles fall on him. At first, he shields his head, then drops his right arm. Suddenly, it's over his head again.
The Trouble With Tribbles - S2-E15
Continuity mistake: During the brawl, as Cyrano Jones watches the action, the glass he quickly raises loses most of the liquid. After he gets half way through the scene, the glass is suddenly almost full.
The Trouble With Tribbles - S2-E15
Continuity mistake: Uhura's image on the conference viewer is of a close up on her face. When the camera looks at the screen, the image is of her head and upper torso. Likewise, when Fitzpatrick is on, first it's his head and torso, then it's only his head and shoulders.
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.