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: At the end of the episode, Selina is wearing a purple vest and grey sweater, but they change to red and purple when she is holding Isis and watching Batman, and they change back to purple and grey as she cuddles Isis.
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'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)
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)
Continuity mistake: When Grace is crying over Harvey, she is holding a picture of him with her left hand while stroking the frame with her right hand. When the shot changes, she is suddenly gripping the frame with both hands. (00:06:15)
Other mistake: The eyebrow on Two-Face's left side is completely illogical. He wouldn't suddenly have an eyebrow that's bigger and bushier than his other eyebrow, and if anything the explosion that created Two-Face would have singed off that eyebrow. The eyebrow is there when the doctor removes Harvey Dent's bandages, so it's not like he put a fake one on for cosmetic reasons, nor would it make sense for the doctor to put a fake one on ahead of his face being surgically repaired. (00:21:15)
Continuity mistake: When we see Two-Face in full for the first time in the previous episode, his left eyebrow is white. In this episode, his left eyebrow is black.
Continuity mistake: When Harvey Dent is scarred in the previous episode, it's only the left side of his face and neck. In this episode and all others with Two-Face, his left hand is also scarred and discolored.
Continuity mistake: The explosion that scars Harvey Dent and creates Two-Face is shown to have scarred and colored him light blue on the entire left half side of his face and neck. However, when he is first shown in the hospital, the parts of the left side of Harvey's face that aren't covered in bandages are still normal, as is his entire neck. (00:19:35)
Continuity mistake: The mud stain on Harvey Dent's suit disappears when he assaults the henchman that kicked the mud on him and then reappears when he is walking away from the scene. (00:04:50 - 00:05:50)
Continuity mistake: The pothole with the mud that Rupert Thorne's henchman kicks at Harvey Dent appears from nowhere. When the henchman is shown kicking the mud, the pothole is located between the police officer behind the henchman's right shoulder and Harvey's assistant Carlos on the henchman's left. However, in the previous shot, the ground shown between the police officer and Carlos contains no pothole. (00:04:35)
Character mistake: Despite being a Greek mythology buff Maxie Zeus says "Vulcan" when he meant "Hephaestus" the Greek god of fire and the forge when he first spoke with Batman.
Heart of Ice - S1-E3
Other mistake: Batman uses a thermos full of chicken noodle soup to defeat Mr. Freeze, and moments later gives Summer Gleason a security tape that incriminates Ferris Boyle. When Batman pulls out both of these aforementioned items, there is a corresponding clicking sound that suggests he pulls them from his utility belt, but both items are far too large to fit inside the belt. They also could not have been simply been hanging from his belt, as Mr. Freeze had possession of Batman's belt a few minutes prior and they were not there. (00:20:05 - 00:20:45)
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)
Answer: Because he stole a chemical from his lab.
But Batman knew that with it, Clayface could permanently retain his shape and Clayface desperately wanted to be Matt Hagen again. In a sense, Batman stopped Clayface from becoming human.