And the Children Shall Lead - S3-E4
Continuity mistake: The stardates of Starnes' entries are 5025.3, 5032.4, and 5038.3 But Kirk gives the stardate of when they arrive at the beginning of the episode as 5029.5, so apparently Starnes made two entries after he died.
And the Children Shall Lead - S3-E4
Continuity mistake: When Gorgon the Angel is on the bridge with the children, the positions of the children are different depending if the shot is from the rear of the children or the front.
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.