Continuity mistake: When Catwoman first encounters Batman during the flashback, her whip is coiled around her shoulder. When the camera cuts back to Catwoman after the shot of Batman, the whip disappears altogether.
Continuity mistake: Batgirl's boots gain and lose heels throughout the climax of the episode.
Continuity mistake: The soles of Batgirl's boots change from light to dark blue throughout the episode.
Character mistake: When Batman uses his magic computer to analyze Langstrom/Man-Bat, lots of lovely gibberish appears on screen, with some notable typos such as "Bat membaaanes", "Sedum Chloride D", "Mammac higi Index Gat harmal nomeaace at padiotion." Your guess is as good as mine for the last one. (00:21:10)
Character mistake: When Batman gets the information from the computer just in time to wrap up the episode neatly, the computer misspells the word "Professor." (00:19:40)
Continuity mistake: In the bat nerds laboratory, Bruce Wayne shows them the tape; his hand suddenly turns between shots. (00:12:55)
Continuity mistake: For one frame during the final battle with the werewolf, the logo on Batman's chest is black and white instead of black and yellow. (00:17:55)
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: When Harvey Dent wakes up from his nightmare, his face is sweating profusely. A couple of shots later and there is no sweat to be seen on his face. (00:02:10)
Answer: She escaped off-screen and created a copy of herself to fool everyone.