Continuity mistake: When Kirk sits down to consult the computer, the big green potted plant on the shelf behind him is there in full shots and missing in close-ups. It's much too large to be completely hidden behind him: if it shows up behind his head in full shot, it should show in close-ups, too, but it doesn't. It's not there. (00:16:30)
Continuity mistake: Kirk punches the Imperial crewman that helps him in the face, but when the guy falls on the ground he's holding his side.
Continuity mistake: A subtle mistake, but when Spock is lying on the table in sick bay and recovers, the readings on the monitor are in the normal range. However Spock, as a Vulcan, produces very unusual readings on the monitors in other episodes.
Revealing mistake: During the fist fight between the transported crew and Spock, the use of stunt doubles in the wide shot is quite obvious.
Visible crew/equipment: When McCoy gives the guard a shot and he and Scotty break into Engineering, you can see a crew member's hand holding a red handle and their bare arm (it's not Scotty), who apparently is helping to open the door. (00:23:00)
Continuity mistake: As Kirk and party dematerialize, Kirk's arms are by his side. As they are briefly seen in the Transporter room, his left hand is up with the communicator.
Revealing mistake: In the close up shots of the mirror Sulu, the poor make up job of the scar on his face is very evident.
Continuity mistake: At the end, Lt. Moreau gives Kirk a report to sign. After signing and giving it back, and after a dialog with Spock, he gets up, goes to Moreau, has the report and looks at it again.
Continuity mistake: As there were two screen used models of the Enterprise, when the ship is seen flipping from one universe to the other and back, the nacelles of the Imperial Enterprise have the solid red fronts with what appear to be antennae.
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.