Deliberate mistake: When Rojan asks Kelinda if she wishes to remain with Kirk, she replies that although Kirk is "most interesting" she wishes to go with him, and the next closeup of Rojan is flipped. (00:48:15)
Continuity mistake: When Scotty gets drunk and tosses an empty bottle away, there's a dubbed in sound of glass breaking, but when he collapses, the bottle is unbroken at his feet.
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.