Continuity mistake: A security guard is recording a silly audition tape-like message. His shadow reaches barely the bottom of the wall, then it's suddenly almost mid-height on it. (00:02:30)
Continuity mistake: When Batman smashes his face against the blimp, in the shot from inside the cockpit there's not much damage, while in the reverse shot it shows how Batman's pointy chin created a rather large web-pattern of damage. (00:18:30)
Continuity mistake: In the bat nerds laboratory, Bruce Wayne shows them the tape; his hand suddenly turns between shots. (00:12:55)
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)
Continuity mistake: Batman goes in detective mode in the room, and scans it for clues. The shattered object on the desk changed size and placement of the pieces. (00:07:50)
Character mistake: When Batman looks up at the computer the data of the burglaries, he says they happened "this week", but the dates are June 28, July 3, and July 13. On the screen there's also a typo; "Buaglary." (00:05:00)
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)
Character mistake: When Batman uses his magic computer to analyze Langstrom/Man-Bat, lots of lovely gibberish appears on screen, with some notable typos such as "Bat membaaanes", "Sedum Chloride D", "Mammac higi Index Gat harmal nomeaace at padiotion." Your guess is as good as mine for the last one. (00:21:10)