Revealing mistake: The shot of the castle on Rigel VII seems to be what Pike sees through his eyes, but in the next shot he himself is in the shot.
Revealing mistake: When the Talosians place Christopher Pike and Vina into the "picnic" illusion (in the countryside on Earth), Pike wanders around marveling at how real it all seems. Well, "real" except for the fact that Pike's body is casting 4 distinct shadows in 4 different directions on the ground, the result of studio set lighting.
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.