Is There in Truth No Beauty? - S3-E5
Revealing mistake: During the fight in engineering, Marvick's kick, throwing one of the engineering crewmen violently back against the wall, misses by an obvious mile. (00:20:10)
Is There in Truth No Beauty? - S3-E5
Revealing mistake: The colorful nebulae of the energy barrier are showing through the hull of the suddenly-transparent Enterprise as it heads back into the galaxy. (00:37:40)
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.