Space Seed - S1-E23
Revealing mistake: During the fight sequence between Kirk and Khan in the engine room, you can see in some shots that it is not William Shatner and Ricardo Montalban fighting, but their stunt doubles.
Space Seed - S1-E23
Revealing mistake: Just before Kirk and Khan fight in Engineering, Khan bends Kirk's phaser pistol in half, but the small hand phaser on top is still functional.
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.