Batman Stands Pat (2) - S1-E14
Revealing mistake: As Batman is about to use his batarang to Mad Hatter's hideout, right before getting caught by him and his henchmen towards the end of the episode, as he moves his cape back, the back part of his costume is open.
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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