Plot hole: Pike says he doesn't want women on his bridge, Number One being the one and only exception, and he keeps ordering Colt off it. His apology to Number One indicates that A) he doesn't think of her as female, and B) she's the only exception to his rule. So how does he overlook the very female crew-woman seated at the science station? (00:06:55)
Visible crew/equipment: When the doctor is mixing the drink and Pike gets up off the bed to accept it, an equipment shadow sweeps across the left side of the screen. (00:03:55)
Revealing mistake: When the laser cannon starts firing at the Talosian rockface, a styrofoam block falls and rolls away on the left side of the screen. After a brief shot of the crew, we see the cannon still firing, and the exact same block falls and rolls off screen on the left again. (00:30:15)
Revealing mistake: In the first illusion, Vina runs down the path from the fortress to Pike. When we cut to close-ups, they're both suddenly standing much closer to the building than before, and the fortress has changed color from brownish orange to white. (00:23:50)
Revealing mistake: Due to a poor edit, there's an odd jump cut and a change of lighting just as the Keeper comes out of the elevator on his way to an attempt to steal the laser pistols from the cell. (00:50:40)
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.