Revealing mistake: In the jail cell scene, when Kirk tears a strap from the bed, his left handcuff is open. It remains open for several seconds, while he tries to conceal it by moving his right hand to block the camera's view.
Revealing mistake: After being put in the cell, when the camera is in a closeup of Spock, you can see the lines in the prosthetic ears, and can easily tell where the makeup is blended into his real ear.
Revealing mistake: As Kirk and company exit through the tunnel, the seams of the wall sections are visible.
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.