Revealing mistake: As Charlie watches the pole lowering into a square hole in the deck, the wood grain of the set piece is visible. The wood has been painted gray/silver to look like metal. (00:06:06)
The Man Trap - S1-E2
Continuity mistake: When Kirk is telling Crater that he needs him and his wife to stay on their ship till he finds out what killed his man, Kirk has his arms crossed. When Crater steps up to him and the angle changes, Kirk's arms are suddenly down at his side. This continuously changes back and forth between shots. (00:18:07)
Revealing mistake: When Kirk holds a golden egg, a seam can be seen on it. (00:43:55)
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.