Other mistake: When Batman listens to the tape left behind by the security guard (and the police's incredibly sloppy investigation) he presses play and not only the tape is at the right point without him having to rewind, but the recording is much different from the actual events and gives him a convenient abridged version. (00:08:00)
Other mistake: Batman is reading the front page of the newspaper, but in the drawings that follow, the paper is right-most, it opens to the left of the page. Gotham is not in Japan. (00:04:50)
Other mistake: On the police blimp, the scanner/radar screen in close-up has a single white circle, but in the wider angle it's two black circles, which are even hand-drawn and thus not perfect circles. (00:01:30)
Answer: She escaped off-screen and created a copy of herself to fool everyone.