Continuity mistake: Kirk and McCoy are in the Exeter's engineering section when Kirk uses the intercom to ask if anyone is aboard. Several shots of the deserted ship follow as his voice echoes off the walls, including one of engineering - with Kirk and McCoy suddenly, mysteriously absent. (00:03:45)
Continuity mistake: At the end, the flag is brought in, and Kirk stands up - but in the next close-up of him, he's sitting down again. Next full shot, he's standing once more. (00:36:25)
Continuity mistake: Near the end, when Cloud William opens "The Book," the red bookmark ribbon isn't in the spot he turns to, until the close-up of the page, when it suddenly appears there. (00:39:15)
Continuity mistake: When Kirk and McCoy join Spock and Galloway on Exeter's bridge, McCoy kneels down and uses his med tricorder with its strap crossed over his shoulder, but in McCoy's closeup the strap is gone, then next shot the strap is once again over McCoy's shoulder. (00:04:25)
Continuity mistake: As the team of 4 energize from Enterprise to go to Exeter, the positions of Spock and Lt. Gallway are altered as they re-emerge on the other side.
Continuity mistake: The background of the cell does not jibe with the positions of Kirk and Cloud William as they fight - where Kirk and Cloud William should have either the cell's bars or the exposed brick wall behind them, there are shots of the opposite wall behind them instead, which is a plastered rock facing.
Continuity mistake: The hilt of the blade Kirk holds against Tracy's throat is close to Tracy's jawbone in the close ups and further away in the long shots.
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.