The Gamesters of Triskelion - S2-E16
Other mistake: When Kirk agrees to fight in the arena at the end of the episode, he and the thralls are warned that touching an opponent's color will result in the loss of a weapon. Kirk does this several times during the fight, but isn't penalized in any way.
The Gamesters of Triskelion - S2-E16
Other mistake: Kirk tosses the Andorian, and as he hits the ground, his shirt comes up and the man's real skin tone is visible.
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.