Flop Goes the Joker (2) - S2-E58
Revealing mistake: After Bruce stops the governor of the mobile, it can be seen that the weights are painted Styrofoam balls.
Enter Batgirl, Exit Penguin - S3-E1
Revealing mistake: The panel that Batgirl makes her entrance through can be plainly seen as a prop mounted on top of the set of stairs she comes down.
Surf's Up! Joker's Under! - S3-E10
Revealing mistake: When the Dynamic Duo are locked in the board blanks, you see the jets where the smoke and flame come out.
A Riddling Controversy (2) - S2-E46
Revealing mistake: When Batman and Robin use their jets to get out of the quicksand, as they fly up, you can see the wires used to pull them up.
The Joker's Provokers (2) - S2-E22
Revealing mistake: When Alfred talks to his twin Egbert, as they face each other, you can plainly see the line dividing the screen so that Alan Napier can play both parts.
An Egg Grows in Gotham (1) - S2-E13
Revealing mistake: A lot of the time, especially in close ups, you can see the line between the bald dome wig and Vincent Price's real skin, as well as the different coloring of skin.
The Bookworm Turns (1) - S1-E29
Revealing mistake: At about the 6:40 mark into the episode, The Bookworm puts an explosive device in the Batmobile which is detected automatically. Batman pushes the auto eject to throw it out of the car. As the special effects prop explodes, you can see the rope it is hanging from as it swings to the side.
Not Yet, He Ain't (2) - S1-E22
Revealing mistake: When being gunned down by O'Hara cops, there are no bullets coming from the cop who gunned Batman down, but he still reacts to it.
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.
Revealing mistake: In this episode and the next one, Robin's stunt double is very obvious from the back, especially in the scene where they enter the Hall of Fame museum.
Penguin's Clean Sweep - S3-E20
Revealing mistake: In any of the close up shots of Penguin, his nose has a completely different skin colour than the rest of his face. Making it very obvious that the actor is wearing a fake nose.
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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