Continuity mistake: Lincoln asks Kirk if they measure time in minutes and Kirk replies "We can convert it." In every previous episode they've always used minutes - their ship chronometers are still set to minutes.
Continuity mistake: During the hand-to-hand fight scene, the stunt double playing Spock gets his hair mussed up, but immediately after the fight, Spock's hair is neatly combed and formed, as it was before the fight.
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.