The Sport of Penguins (1) - S3-E4
Deliberate mistake: After the episode intro, in the first shot we see the words "The New York Public Library" above the entrance to the library, where Barbara Gordon works. However, it's stated in S3xE1 that she works at Gotham City Library, and even in this episode when Penguin listens to the news about the bomb, it's noted as the Gotham Library. (00:02:00)
The Unkindest Tut of All - S3-E6
Deliberate mistake: When Batman has figured out King Tut's plot to steal ancient Egyptian scrolls from the Gotham City Library, he and Robin rush away, and in the shot of the library exterior, the words "The New York Public Library" is quite noticeable above the entryway. (00:18:00)
Deliberate mistake: At the start of the episode the Boy Scout asks why the Cossacks are in Gotham City, then a moment later as narrator William Dozier says, "At the Gotham City Museum" the closeup we see shows "Los Angeles County Historical and Art Museum" over the museum doors.
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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