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.
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.