Continuity mistake: When Kirk confronts Spock in his quarters, Kirk asks if it's something only his planet can do for him, then Kirk uses his left hand to grab hold of Spock's arm as he drops the stylus, but in the closeup it's Kirk's right hand holding Spock's arm up, and that stylus is also back in Spock's raised hand. (00:12:25)
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)
Continuity mistake: Just before T'Pring calls for the challenge, there's a wide shot of her going toward the gong. Then they cut to a closeup and she is standing beside Stonn, and then she starts moving toward the gong 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.