Continuity mistake: Batgirl's cape changes length throughout the episode. It goes from reaching her ankles to her hips.
Other mistake: When Catwoman scratches Batman's face in the flashback, her fingers and claws stretch comically.
Continuity mistake: During the flashback, Catwoman's whip disappears and reappears on her belt in a couple of scenes.
Continuity mistake: When she was pulling Daggett up, Batgirl briefly gains pupils when she says "Catwoman, wait."
Continuity mistake: Harley's shoes are poorly drawn when she dances in Dr. Leland's office.
Continuity mistake: Catwoman/Selina gains and loses her pupils throughout the episode.
Continuity mistake: Batgirl and Catwoman briefly gain pupils in one shot of them during the Stacked Deck fight, despite not having any throughout the episode. (04:00:39 - 04:41:24)
Continuity mistake: When Riddler burns his costume, he's wearing his purple gloves, but after throwing his green jacket into the fireplace, his gloves disappear entirely. (04:25:03 - 04:29:59)
Other mistake: When Alfred serves Bruce coffee at the end, there's no steam coming from the coffee pot or Bruce's mug when Alfred pours the coffee into mug.
Continuity mistake: The 10/6's on the Mad Hatter's mind control cards come and go throughout the episode.
Continuity mistake: Riddler's gloves disappear briefly after Batman confronts him at his party.
Continuity mistake: The soles of Batgirl's boots change from light to dark blue throughout the episode.
Continuity mistake: Batgirl's boots gain and lose heels throughout the climax of the episode.
Continuity mistake: When we first meet Harley Quinn, her gloves are white before becoming their normal colors of black and red in the next shot.
Continuity mistake: Both of Harley's shoes are red as Batman holds her after rescuing her from falling.
Continuity mistake: During his introduction Scarface's scleras go from light yellow to white then back to light yellow.
Continuity mistake: When Poison Ivy is introduced in her trademark green costume, she's bare legged. Yet a few shots later, she's suddenly wearing green tights. While she's offscreen for a brief period, there's not enough time between the shots for her to have put them on.
Continuity mistake: The 10/6th on the Mad Hatter's mind control cards come and go throughout the episode. An example is when he first is shown holding them they're blank. Then when he decides to use them on his date with Alice they've suddenly got the 10/6th.
Revealing mistake: When the passengers are evacuating the sinking ship after the bomb goes off, there is a shot shown from above, of passengers running up the stairs. Many of the character designs for the passengers are repeated throughout the shot. For example, a blonde woman in a purple dress can be seen three times in the shot. (00:02:36)
Continuity mistake: Scarecrow's shoes are light brown in most of the episode. Yet once he's back in his cell they're suddenly dark grey.
Answer: She escaped off-screen and created a copy of herself to fool everyone.