Other mistake: Kirk and Spock stun two Klingon guards, yet despite being unconscious, the guard on the left jumps from the balcony and lands feet first on the ground. If he were really unconscious he would have simply tumbled down. (00:36:20)
Other mistake: When Kirk is lecturing Ayelborne in the council chamber, the actor behind him is mouthing Kirk's dialogue.
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.