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 spheres or perforated vents at the nacelles' ends.
Smack in the Middle (2) - S1-E2
Deliberate mistake: Ignoring that its very unlikely all of Jill St. John's copious red hair would fit under a wig that passes for Robin's hair, it's impossible that it would emerge from under that wig looking as full and perfectly styled as it does when she's in the Batcave.
The Garden of Evil Affair - S1-E8
Deliberate mistake: The bad guys chase Mark through a movie studio backlot past a London bus with a large red "Out of Service" sign on its side. During the ensuing shoot-out scene, the film is reversed for some reason, and the sign on the bus is suddenly backwards. (00:24:20)