Deliberate mistake: When the decoyed Enterprise heads back to Capella, the special effects shot is reversed to indicate that it's going back in the other direction. Unfortunately, this gives us two brief shots of the ship with the registration numbers backwards. (00:37:40)
Deliberate mistake: After one of the enemy villagers stabs Nona, during the ensuing fight when Kirk does a flying dropkick on a villager, this semi-closeup and the next wide shot are both flipped shots - the leather band is on Kirk's left upper arm, instead of his right. (00:46:15)
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)
Deliberate mistake: When Spock is brought to the Yang ceremony to join Kirk and McCoy, after Spock responds that although he is weak their "need for departure is even more immediate," the very next closeup of Kirk is a flipped shot. (00:34:15)
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.