Audio problem: About a minute or two into the episode, Captain Kirk says "That's incredible" but his mouth doesn't match the words.
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.
Who Mourns for Adonais? - S2-E2
Audio problem: At the temple, as Kirk goes to call the ship, he flips the communicator to open it, as he usually does. However, he has to flip it twice to get it to open, but the sound of the channel opening is heard from the second he starts.
Audio problem: As Commodore Stocker freezes up on the bridge, before the cut to sick bay, the bridge is shaken by a Romulan blast, but the sound is absent.
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.