Star Trek (1966) - 7 mistakes in whole show

Deliberate "mistake": Special effects of the ship in space were very expensive in the 60s and couldn't be wasted. So when a larger model was built with slightly different nacelles, shots of both versions became common, even within the same episode. This is why the Enterprise sometimes had red needle-tipped nacelles and sometimes lighted "spinning" ones, and in aft views she had either round white balls or perforated vents at the nacelles' ends.

Plot hole: "The Cage": 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?

Visible crew/equipment: "The Cage": 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.

Revealing: "The Cage": 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.

Revealing: While the interior sets for the shuttle craft provided adequate room for the actors to stand, the mock-up built for exterior shots was undersized, and too short to stand up in by several inches. So when entering or exiting the shuttle, the actors always had to duck.

Revealing: "The Cage": 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.

Revealing: "The Cage": 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.