Continuity mistake: When Selina dons her Catwoman costume, she pulls on her mask which was detached from her costume like a face mask, but later on when she returns to her apartment after the museum robbery, she removes her mask which is now attached to her costume like a hood.
Continuity mistake: When Selina talks to Scarface in the limousine, her eyebrows change from black to blond back to black again between shots.
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 cowl, cape, gloves, and boots are black in this episode, but in Shadow of the Bat Part II and Batgirl Returns, they are now blue and remained that way onwards.
Continuity mistake: Batgirl and Catwoman are depicted without pupils, but in one shot during the fight at the Stacked Deck, they briefly gain pupils when Batgirl says "I think it's closing time."
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)