Continuity mistake: There is a jump cut at the beginning when Batman and Robin are being lowered into the vat of wax, where all of a sudden, Batman is trying to wiggle his legs free.
Continuity mistake: At the beginning, in the wide shot of Batman and Robin over the candle dipper, Riddler is standing with his back towards them, but in the close-up, he is facing forward.
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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