Continuity mistake: When Kirk is facing the Horta he has his phaser in his right hand when seen from the front but when seen from behind he has his communicator in his left hand and no phaser. (00:31:00 - 00:38:00)
Continuity mistake: After his initial mind meld with the horta, Spock tells Kirk, "That's all I got, Captain: waves and waves of searing pain." A minute later, he says that it's "a highly intelligent, extremely sophisticated animal" that calls itself a horta. Apparently, waves of searing pain were not all that he got after all. Unlike Spock to be so imprecise.
Continuity mistake: After McCoy checks the Horta, he approaches Kirk with his tricorder in his left hand. The scene cuts to McCoy and Kirk and now McCoy's tricorder is in his right hand.
Continuity mistake: Spock and Kirk both arrive at the sizzling remains of a red shirt crewman, standing close together, but the next shot of the crewman's remains shows only one set of legs at the site (presumably Spock's), not two.
Continuity mistake: As Kirk is crawling through the tunnel leading to the Horta's nest, a tight view from his left side shows light shining on his face and darkness behind him. When the shot changes, though, to the view from the nest, there is light behind him and darkness on his face.
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.