Other mistake: At the end, Kirk teases Spock twice specifically about letting himself be hit on the head in order to determine which Kirk was genuine. But the phony Kirk never hit Spock on the head. He merely pushed Spock over and attacked the real Kirk. Clearly, the action sequence wound up differing from the scripted dialogue, and no one noticed. (Also clearly, Kirk is not speaking metaphorically here.) (00:45:30 - 00:49:20)
Other mistake: The only way to beam up to the ship is to repeat the chess counter move after ASKING to be beamed aboard. After the two Captain Kirks fight ends with Spock stunning Garth with the phaser, Spock contacts the Enterprise. After saying "Spock to Enterprise, and hearing Scotty say back to him "Scott here", Scotty says" Queen to Queen's level 3" without Spock requesting to be beamed aboard or even waiting to see what Spock wanted in the first place. (00:46:56)
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.