Visible crew/equipment: After the Klingon vessel's attack on the Enterprise, while returning fire just as Kirk orders to maintain firing range at 100% dispersal pattern, the set's unfinished wood plank with grey paint drip marks can be seen at the bottom of the screen. Additionally, at the end when Spock goes to stand beside Kirk's chair (also when he walks away) the actor's mark can be seen on the floor by Spock's feet.
Visible crew/equipment: When Kirk is thrown into jail with Spock you can see the movement of the entire blue crash mat used to break his fall.
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.