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.
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)
Answer: She escaped off-screen and created a copy of herself to fool everyone.