Continuity mistake: In the opening scenes, Sulu's retractable viewer isn't there when the Klingon ship approaches on the view screen. But a moment later in a closer shot, the viewer is suddenly in front of him, fully extended. (00:01:05)
Continuity mistake: In the turbolift, Chekov is standing to the left, but when the door opens he has moved to the right and exits behind Spock. (00:10:40)
Revealing mistake: Chekov covers Mara's mouth with his hand when he assaults her in the corridor. Kirk intervenes and throws Chekov against the opposite wall. Brown streaks form where Chekov's hands hit the wall, most likely from the brown makeup used to create Mara's skin tone. (00:32:20)
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)
Continuity mistake: At the end when the entity left the Enterprise, it came out of the secondary hull, however it left from the engineering dept. The Engineering dept. is located in the back of the primary hull.
Other mistake: As Kirk and party duel against the Klingons, there's a heavy-looking round conduit on the wall right before the turbolift door that gets knocked down so it stands as a big flower pot. A moment later, it's back in position.
Continuity mistake: The first time we see the ship travelling at Warp Nine, it is moving in a level, straight path. Next time, the rear end is elevated above the line of flight. The next time, it's moving in level flight again.
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.