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.
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.
Factual error: After he becomes agitated with his doctor, Harvey Dent is able to toss the doctor across the room with one hand while sitting in his hospital bed. Harvey Dent/Two-Face does not possess superhuman strength, and lying in a hospital bed for several days would have only weakened him, so throwing his doctor across the room like that would not be possible. (00:20:50)
Factual error: It doesn't seem likely Maxie Zeus could've survived being both electrocuted and hitting concrete real hard at least without some serious injuries.
Factual error: The note the Joker has that says Charlie has changed his name to Don Wallace lists his address as 12 Marigold Lane, Springdale, Ohio, a city near Cincinnati; however his area code is listed as 614, which is the Columbus, Ohio area code.
Answer: She escaped off-screen and created a copy of herself to fool everyone.