Continuity mistake: Arkham Asylum cells are different in different episodes - in Fear of Victory and Fire From Olympus they come with big windows. Whereas in others like Dreams in Darkness and Harlequinade they're smaller with small windows in the doors that are sliding open kind.
Continuity mistake: In some episodes like Trial the inmates are wearing prison uniforms while in others like Fear of Victory they're wearing their costumes. Another thing is the prison uniforms constantly change color, in some episodes they're light grey, others light blue, then in some light purple.
The Cat and the Claw (1) - S1-E1
Continuity mistake: In the beginning when Catwoman lands, she's seen putting her whip away. In the next shot looking through the window, she's rolling up her whip.
Continuity mistake: A security guard is recording a silly audition tape-like message. His shadow reaches barely the bottom of the wall, then it's suddenly almost mid-height on it. (00:02:30)
Continuity mistake: Batman goes in detective mode in the room, and scans it for clues. The shattered object on the desk changed size and placement of the pieces. (00:07:50)
Continuity mistake: In the bat nerds laboratory, Bruce Wayne shows them the tape; his hand suddenly turns between shots. (00:12:55)
Continuity mistake: When Batman smashes his face against the blimp, in the shot from inside the cockpit there's not much damage, while in the reverse shot it shows how Batman's pointy chin created a rather large web-pattern of damage. (00:18:30)
Heart of Ice - S1-E3
Continuity mistake: When Mr. Freeze's henchman Johnny gets his legs frozen, he is wearing pants and shoes. Later when Johnny is inside a water tank in the Batcave in order to thaw the ice, he has been stripped down to his boxer shorts. While it's possible for Batman to remove Johnny's pants above the freeze-line by cutting them away, he would still have remnants of his pants underneath the ice, but when the ice is thawed, his legs and feet are bare. (00:05:45 - 00:08:05)
Heart of Ice - S1-E3
Continuity mistake: When Mr. Freeze's henchman Johnny gets his legs frozen, an ice "bridge" connects the gap between his feet. A few shots later and the connective ice is gone, making it look like he is wearing boots made of ice. (00:05:45 - 00:07:00)
Heart of Ice - S1-E3
Continuity mistake: In the wide shot of Batman hanging upside down in Mr. Freeze's lair, his face is blank and the bat outline from his chest emblem is missing. (00:14:10)
Heart of Ice - S1-E3
Continuity mistake: When Batman breaks free of his ice handcuffs, the colors on his chest emblem are inverted. (00:15:30)
Heart of Ice - S1-E3
Continuity mistake: When Mr. Freeze is running towards the fire hydrant, it is partially covered in a layer of ice. When the shot changes, the ice has disappeared altogether. (00:18:15)
Continuity mistake: When Clay-Face makes things like crab claws they're red. Yet later on when he fights Batman again in the TV station they're light brown.
Continuity mistake: The clay used to bind Germs goes from a creamy light brown to dark brown.
Continuity mistake: Clayface has clay in the shape of the right hand on his chest when fighting Batman. A few seconds later it's suddenly in the shape of the left hand.
Continuity mistake: Stromwell crushes under his fist the remote control - not bad for a supposed old man! But the remote is also completely gone in the next shot. (00:02:10)
Continuity mistake: Thorne's henchman that stayed behind to check out the aftermath of the explosion is wearing a flower on the lapel of a white coat the first time we see him, and then a gray coat with no flower when he sneaks away to report to his boss. (00:10:15 - 00:11:20)
Continuity mistake: Stromwell tosses on the desk the binder with the information; it does not have a label on the cover, then it does. (00:14:40)
Continuity mistake: Batman throws a chair and shatters a window. You can see that there is basically no part of the frame nor glass left at the bottom, but when Stromwell looks outside and when Batman gets back in the office, part of it is still standing. (00:15:55)
Continuity mistake: The henchmen spot Stromwell as he makes a run for it through the train yard. Before the chase begins, Thorne gets in frame in a close-up, and he has eyebrows matching the white of his hair instead of his usual black. (00:17:15)
Answer: She escaped off-screen and created a copy of herself to fool everyone.