The Ultimate Computer - S2-E24
Plot hole: When M-5 destroys the ore freighter, Dr. Daystrom says, "Fortunately, it was only a robot ship." But Daystrom wasn't on the bridge yet when Spock announced that fact. He didn't have any way of knowing that the freighter was unmanned. (00:23:00 - 00:25:05)
The Ultimate Computer - S2-E24
Visible crew/equipment: After M-5 fires on the other starships Daystrom speaks to M-5 about the murders, then when Kirk walks over to Daystrom and tells him the M-5 must be destroyed, the shadow of the moving boom mic is visible over Daystrom. The white tape mark is also visible on the floor near Uhura's chair, where McCoy had been standing earlier. (00:42:15)
The Ultimate Computer - S2-E24
Continuity mistake: During the scene with the ore freighter, there are four closeups of Spock while he's bent over the scope at his station, and in the background behind Spock we can see Kirk and others on the bridge are gone. It also occurs in the earlier scene during the encounter with the two starships. (00:24:00)
The Ultimate Computer - S2-E24
Audio problem: After trying to change course, Sulu calls Kirk. Kirk says "Kirk here", and then you hear the click of the comm button being hit.
The Ultimate Computer - S2-E24
Continuity mistake: When Sulu is first reporting the M-5 movements, Kirk's hand alternates between being up at his temple and down by his mouth, too quickly to be real.
The Ultimate Computer - S2-E24
Continuity mistake: The doctor and Spock are facing each other, the camera angle changes and they are suddenly shoulder to shoulder. (00:26:50)
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.