The Trouble With Tribbles - S2-E15
Revealing mistake: When Kirk and Spock answer the intercom in the ship's corridor, Spock's uniform has a large brown coffee stain on the front. (This was digitally removed in the DVD release, but is still visible in the newly-syndicated "computer enhanced" version.). (00:17:00)

The Trouble With Tribbles - S2-E15
Revealing mistake: When Kirk finds his position on the bridge occupied by the Tribbles, he calls for Dr. McCoy, and as he arrives, Kirk thrusts some of the Tribbles under his nose. In the shots where Kirk's face is seen, one of the Tribbles he is holding features a visible seam.
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.