Continuity mistake: The Organians cause all the weapons to overheat, and everyone drops them to the floor. When Kor moves to the desk to call his ship, though, he's wearing his disruptor. It's gone again when he returns. (00:41:45)
Continuity mistake: When Kirk orders the crew to fire phasers; the exterior shots show the ship firing torpedoes, and torpedo explosions flashing out in space.
Continuity mistake: Kirk has a sunburn on his face and chest (it appears to end partway down his chest-most noticeable in the scene shortly after his identity is revealed to the Klingons). First of all, how does one get a sunburn while flying through space (and one that does not match the pattern of the uniform). If one wants to explain it away as being from a recent Shore Leave or Enterprise tanning bed, the issue still remains that the intensity of the sunburn changes as the episode continues.
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.