The Penguin's a Jinx (2) - S1-E4
Continuity mistake: When the Penguin goes to Wayne Manor to put Batman and Robin to sleep with the gas from his umbrella, just before he shoots the orange gas at Robin's suit of armor, there's a quick shot of the armor's helmet. The problem is that there's already an orange stain on the face of the helmet from the orange gas that comes out of the tip of the umbrella, even before Penguin shoots any gas. (00:19:15)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: At the beginning of the big fight with Penguin, everyone is doing some fencing with the umbrellas. The guy with the caveman face on the left switches stance depending on the camera angle; he's lunging forward waving his umbrella with one arm in the frontal views, and he's in a guarded position in the overhead shots. (00:21:20)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Robin jumps on a table, dodges a swing and gives a (really weak) kick to his adversary. Cut, and he is nearly tripping over two umbrellas on the table he is standing on, suddenly appeared out of nowhere. (00:21:40)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Batman punches Hawkeye with a BAM; in the closer view Robin is not where he is supposed to be (next to the elevator, where he was sent reeling by the punch and where the action takes place in the following shot). (00:21:45)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Batman sends Swoop into the wall with an "OOOOFF!" onomatopoeia. The impact knocks down from the shelf a bunch of umbrellas that fall on the poor guy, but as the scene goes on, the floor is clean and the umbrellas are still on the wall rack. (00:21:30)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: When the umbrella fight erupts, the red suitcase with the money changes position on the corner of the counter (basically rotating of 90°). (00:21:20)
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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