Catwoman Goes to College (1) - S2-E49
Continuity mistake: When they first go to the bat poles, Bruce is on the right. The next shot at the bottom, Bruce/Batman is on the left and Dick/Robin is on the left. They switched sides. It has happened throughout the series.
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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