Revealing mistake: Isis the cat was disinclined to hold still for special effects shots. When Gary Seven beams off the Enterprise with the cat in his arms, the position of her head jumps several inches as they're dematerializing. (00:10:10)
Revealing mistake: After Scotty finally locates Seven on the gantry while he's tampering with the rocket, it cuts to a quick shot of Kirk and Spock, then in the following shot of Roberta when she turns the vault's combination locks, the stunt wire is visible behind her as it moves up to turn the door's wheel handle. (00:35:25)
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.