
The Joker's Hard Times (2) - S2-E38
Continuity mistake: At GCPD HQ, when Commissioner Gordon decides to call Batman he removes the Batphone's acrylic dome cover and lifts the red receiver, still holding it when Joker shows up. Then, when Joker announces his next target is Libra the scales, in the next shot from a different angle, the Batphone is now untouched under the acrylic dome, between shots. (00:02:55)

The Joker's Hard Times (2) - S2-E38
Visible crew/equipment: After Joker and his henchmen steal the statue, it cuts to Commissioner Gordon and Chief O'Hara as they recover from their shock paralysis, and when they walk over to Gordon's desk, the wheel of filming equipment is visible at the right side of the screen. (00:04:55)

The Joker's Hard Times (2) - S2-E38
Continuity mistake: After Joker enters Commissioner Gordon's office, Gordon and Chief O'Hara walk over to the window, and the Batphone table is behind them, beside Gordon's desk. Then Joker makes two "quick-frozen cops" and runs off to snatch Justice, leaving Gordon and O'Hara immobile. When their shock paralysis wears off, Gordon and O'Hara rush over to Gordon's desk, but the Batphone table and the Batphone have vanished (note the rug's pattern). (00:03:00 - 00:04:55)

The Joker's Hard Times (2) - S2-E38
Revealing mistake: When Joker pays another visit to Commissioner Gordon and Chief O'Hara, Joker's holding his wand, and in the shots from outside the GCPD office window we can see the wire cable dragging behind Joker, which is attached to the wand and providing its power. During these shots, the actors' small white tape markers are also visible on the rug, beside the Batphone table. (00:03:00)
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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