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.

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)
Continuity mistake: The Joker reads “Charles Michael Collins” from Charlie’s card, but later, when he shows it to the camera, there is no middle name on it.
Answer: Because he stole a chemical from his lab.
But Batman knew that with it, Clayface could permanently retain his shape and Clayface desperately wanted to be Matt Hagen again. In a sense, Batman stopped Clayface from becoming human.