Revealing mistake: When Batgirl hands Batman the rope, just as he tells her to concentrate on the Indian fakir command, above Batman's head we can see the glistening wire that will be used in the stunt. Then, after Batman and Batgirl have escaped the dungeon Robin rushes up and asks how they did it, and when Batman reiterates the Indian fakir command for Robin, we can see the wire attached to the rope. (00:15:55 - 00:18:05)
Revealing mistake: The strings used to operate the bees attacking Robin are visible.
Answer: It's wasn't unusual for multiple actors to play one character on this show. The villains on the TV Batman were played by guest stars, not regular cast members. George Sanders, Otto Preminger, and Eli Wallach played the part at various times. They may simply have only wanted to play the part once or twice, or they were later tied up with other projects, making it necessary to cast someone else. Other characters, like Catwoman, were also played by more than one actress.
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