Revealing mistake: Batman drives out of the batcave alone. The first bit of stock footage of the car leaving the cave does indeed show him alone in the batmobile. But the very next stock shot of the car speeding down the dirt road shows us Robin sitting in the passenger seat.
Revealing mistake: Most of the first season's episodes follow a standard outline where, after the opening credits, Batman and Robin arrive in the Batcave via the Batpoles, run and enter the Batmobile and drive off, along the winding, dusty roads toward Gotham, then arrive in front of City Hall, exit the car and run up the stairs. But very quickly it becomes obvious that every bit of this is the same footage used over and over. As they get in the car, it's on a black platform which vanishes as the car starts moving. The same cloud of dust appears as the car's rear heads into the distance on the winding road, and the same crowd of people are in front of City Hall, nearly every episode.
Revealing mistake: The Batcave was a stage set with no real exit for the car. So in many episodes where a shot is looking into the cave from the darker tunnel as the Batmobile approaches and passes to our right, the rear end of the car jumps upward and tire skid marks appear on the floor as the driver slams on the brakes to avoid hitting the studio wall that is out of the shot, while the audio suggests the car is still accelerating.
Revealing mistake: During the fight in the museum, one of Catwoman's henchmen slams into the wall beside a window. The set wall buckles and caves in, leaving the bottom edge of the window bent and jutting out. A few shots later, though, both wall and window have repaired themselves.
Revealing mistake: When Bruce, Dick and Aunt Harriet get into what's supposed to be an elevator, there's solid concrete under the sliding doors where there should be a break separating the lift car from the building's floor. It's visible again in Part 2, when Batman and Robin use the same elevator.
Revealing mistake: The crowd scenes during what is supposedly a Gotham City University student protest rally are inserts of rather blurry old stock footage. Not only is the mob far too large for a mere college rally, the footage is in black & white, while the rest of Batman is in color. Bit of a dead giveaway.
Revealing mistake: At about the 6:40 mark into the episode, The Bookworm puts an explosive device in the Batmobile which is detected automatically. Batman pushes the auto eject to throw it out of the car. As the special effects prop explodes, you can see the rope it is hanging from as it swings to the side.
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