Continuity: Molly is about to disguise herself as Robin. But the wig she's holding isn't even remotely the same color as Robin's hair. Of course, as soon as she puts it on and transforms herself, the wig darkens and becomes Robin's actual hair.

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.

Continuity: Just after the Joker tells the fake Robin to turn on her homing beacon, a quick shot of the Batmobile approaching shows it isn't glossy black with cherise red trim as normal, but is instead flat black with white trim. This footage was from pre-series testing, painting the car different ways to see how it would look best on film, but somehow this footage was actually used in the episode by mistake.