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)
Heart of Ice - S1-E3
Other mistake: When Batman is watching the security footage of Victor Fries' accident, at first Fries is addressing the camera directly which follows him and pans according to his movements and Ferris Boyle interrupting him, which would suggest a second person was in the room with a handheld camera. But after Ferris Boyle enters the room and orders Fries' experiment terminated, there are several cuts from various angles in the room suggesting surveillance cameras. The surveillance style footage also often conveniently cuts to the face of whichever person happens to be speaking or will cut to a certain angle in order to put emphasis on the action, all of which would require multiple mounted cameras and purposeful editing by either Boyle or one of his subordinates, which would be completely illogical since they don't want anyone to see the footage in the first place. (00:12:20 - 00:13:55)
Factual error: Batman is in Japan and tracks down Kyodai Ken by using Caller ID, which returns a seven-digit "555" number. Telephone numbers in Japan have 8 digits.
Continuity mistake: Riddler's gloves disappear briefly after Batman confronts him at his party.
Other mistake: Melissa Manchester and Neil Ross voice minor characters in this episode. The end credits list them like this though; "Additional Voices - Melissa Manchester as Neil Ross." It should have been "And", of course. (00:21:55)
Factual error: A vital part of the plot's resolution is based on the fact that the reading activity of the brain happens in the right hemisphere, while the dream activity is localized in the left half, making thus impossible to read during a dream. Besides anecdotal experience that says the contrary, this 'fact' is not supported by medical studies, which in fact contradict it. There is no hard distinction, it varies greatly between individuals and even going by those studies who could be seen as supportive of the theory, reading would not be impossible and speaking would be just as hard.
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)
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
Revealing mistake: When Batman - disguised as a security guard - opens his utility belt, the belt opens and shows a configuration of buttons and a split-second later, a key card materializes out of thin air in front of the buttons. (00:11:30)
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)
Plot hole: When Two-Face and his men have broken into the new D.A.'s office to find dirt on Rupert Thorne, one of his men finds a file detailing Thorne's record of Swiss bank accounts, money laundering, blackmail and payoffs that Two-Face tried for years to subpoena when he was D.A. When Thorne finds out that Two-Face has the file, he states that he will be ruined if Two-Face gives the file to the police. If Two-Face tried unsuccessfully for years to subpoena the file, then in all likelihood that means Thorne paid off the right people to prevent the subpoena from happening, so Two-Face giving the file to the police shouldn't be a problem for him. Additionally, if giving the file to the police would be all that it would take to bring Thorne down, then the new D.A. could have already done so. If the new D.A. was also paid off by Thorne, then it wouldn't make sense for Thorne to allow the D.A. to keep the file since they could easily lose the file or even double-cross Thorne. (00:10:45 - 00:14:20)
Continuity mistake: The broken window pane on the door to the District Attorney's office changes slightly from shot to shot. When first shown, the break in the glass extends all the way up to the letter "L" in the word "law." When the shot changes, the break in the glass is nowhere near the letter "L." Also, the letter "W" in the word "law" is missing entirely, even though the break in the glass suggests a portion of the letter would still be intact if the letters were painted on the glass, as is standard. (00:10:25)
Other mistake: When Two-Face is looking at the picture of Grace in his wallet, you can see he has a credit card that says Two Fa[ce]" on it. A bank wouldn't issue a credit card to someone under that kind of pseudonym, and it would be very foolish for a known criminal to use a credit card since any purchases can be tracked. Even if it was a company credit card for a dummy corporation, it would be equally foolish for Two-Face to have a dummy corporation named after himself. (00:08:05)
Answer: She escaped off-screen and created a copy of herself to fool everyone.