Continuity mistake: When Batman starts the Bat-Turn, the parachutes are shown deploying on a 6-lane major roadway (3 lanes in each direction) in a very open area, but after completing the 180-degree turn, the car is shown driving away from the crumpled chutes on a much narrower side street among tall buildings.
Trivia: The 1966 T.V. Batmobile was created from a decade-old "concept show car" designed and built in 1955 by Ford's Lincoln Division. It was called the Lincoln Futura, and was originally a pearlescent pale green. After several years on the car show rounds (and an appearance in one movie, repainted red), it was sold for $1 to George Barris who stored it outdoors for 6 years. When FOX called looking for Barris to build a car for the show, they gave him 3 weeks, so he grabbed this already-weird looking car he had out back, sketched a few changes and passed the physical work to Bill Cushenberry. It was finished on time and the rest is history.
Continuity mistake: 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.