Revealing mistake: The Batcave was a stage set with no real exit for the car. So when the car exits for the first time here, one shot is looking into the cave from the tunnel as the Batmobile approaches and passes to our right. Just before the shot ends, 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. (00:03:40)johnrosa
Continuity mistake: When the Batmobile arrives on the pier, it's parked with its front end facing open ocean (against the orange contraption on the dock) and its tail toward dry land. But when Batman and Robin return and phone the Navy, the car has reversed direction (tail now against the contraption). It's not likely Batman would arrive back at the pier, start the car, turn it around, park in the same spot, shut the car off, reopen the doors and then make a call, only to then drive away. (00:20:10 - 00:28:15)johnrosa
Continuity mistake: As the Batmobile arrives at the pier, it turns into a parking space, one of two available between a green VW Beetle and a white station wagon. In the close-up as Batman and Robin exit the car, the spaces on both sides of the Batmobile are empty. Judging by the location of the "Moby Dick" sign at the edge of the pier, the white wagon has disappeared. (00:59:05)johnrosa
Revealing mistake: When the Batmobile emerges from the Batcave for the first time, the guard rail lays down and the car turns toward our right, disappearing in a cloud of dust. Watching carefully reveals the dust is being kicked up because the car was over-accelerated by the stunt driver, and spun out, heading back into the roadside brush. (00:03:45)johnrosa
Revealing mistake: When Batman brings the Penguin to the Batcave the Batmobile skids to a stop on the gray floor. It then begins to rotate in the next shot and it's now on a black platform. When the Penguin emerges from the car and walks toward the rear of it, the platform is obviously gone. (01:06:10)johnrosa
Other mistake: If you look closely at the top left part of the screen, you can see Penguin hit Robin with the umbrella and turn to the zip line in a far shot of the fight. One shot later, just after Batman kicks a pirate off the side of the sub, the same act is repeated when the camera is focused on the two of them.
Deliberate mistake: When the fight first begins on deck of the sub, a henchman jumps from the hatch and picks up a wrench that was lying on deck. If the sub just surfaced, where did that wrench come from?