Factual error: When Bruce, Dick, and Aunt Harriet are looking at the globe, Bruce corrects Dick's mistake about Lima being the capitol of Ecuador and says "No, as you can see, I was right. It's the capitol of Peru." and points to the globe to show him. Based on the position of Europe facing the camera, he's actually pointing to somewhere in northern Canada. (00:02:35)
Other mistake: Riddler says that his "universal wax solvent" can eat through anything. Which begs the question, just what is that vat he cooks the stuff up in made of? We see the wax burn through solid steel vault doors. So it also ought to be eating through the vat, the floor and the bedrock, and sizzling its way down to the Earth's core. (00:07:00)
Visible crew/equipment: Outside Madame Soleil's, when Riddler notices the Batmobile he rushes up to it with Tallow following behind, and the chalk T-mark is visible on the ground at Tallow's feet. As this shot continues, when Tallow warns Riddler about the Batmobile's burglar alarms, the reflection of the boom pole/mic is visible on the glass. (00:19:10)
Revealing mistake: While Batman and Robin are tied up and suspended over the enormous candle dipper vat, there are stunt wires leading to under their capes. (00:21:00)
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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