Deliberate mistake: So that he can look in the right direction, toward Lincoln, a shot of Kirk is reversed before the first battle, putting his uniform insignia on the wrong side. (00:25:45)
Is There in Truth No Beauty? - S3-E5
Deliberate mistake: While Miranda is with Kollos, McCoy tells Kirk that he didn't reveal her secret because he respects her privacy, then when Miranda steps out of the room and concedes to obey, the next closeup of Kirk is a flipped shot. (00:34:05)
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.