The Corbomite Maneuver - S1-E11
Continuity mistake: Spock states that the Fesarius (Balok's ship) "must be a mile in diameter". Yet any one of the small spheres that make up the Fesarius dwarfs the Enterprise. If the Enterprise is about 300m long, the Fesarius would have to be around 6 km in diameter - considerably larger than a mile.
The Corbomite Maneuver - S1-E11
Continuity mistake: As Balok's 10 minutes are counting down, McCoy comes onto the bridge wearing a standard blue velour uniform. A few minutes later, when Spock says he can bring up Balok's image, McCoy is suddenly wearing his medical tunic with the different fabric and collar. Then when Bailey starts losing it, McCoy is back in the regular velour costume again.
The Corbomite Maneuver - S1-E11
Continuity mistake: After they've blasted the cube, Kirk and Spock are discussing repairs on the bridge. Spock's earpiece is in place one minute, but vanishes the next when the camera angle changes. (00:13:30)
The Corbomite Maneuver - S1-E11
Continuity mistake: As McCoy first appears from the elevator behind Kirk, then follows him in, his hairline changes from a widow's peak to straight across.
The Corbomite Maneuver - S1-E11
Continuity mistake: When the cube first meets the Enterprise, it's spinning clockwise on its axis. Later, it's spinning counter-clockwise.
The Corbomite Maneuver - S1-E11
Continuity mistake: While beaming to the alien ship, McCoy has his hands on his knees. When materializing, they are beside his thighs.
The Corbomite Maneuver - S1-E11
Continuity mistake: As the bridge shakes after the object is destroyed, Bailey's chair goes from tilted to upright between angles.
The Corbomite Maneuver - S1-E11
Continuity mistake: The cube holding the ship in place is spinning counter clockwise, from left to right, on its axis. When the camera is looking at the bridge, the colors are going from left to right, rather than right to left to match the cube's movement.
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.