Other mistake: While fighting Mr. Freeze (and Bane) at the Gotham Observatory, Batman, Robin & Batgirl all have batsuits on, with silver bat (or robin) symbols on their chest. But while they are giving Alfred the cure to Stage 1 of McGregor's Syndrome, for some reason they have changed clothes before giving him the cure. Because now (other than the fact that they have all taken off their masks) Robin has on his original robin suit (with the red robin symbol across his chest) and Batgirl has on a gray t-shirt.
Other mistake: When Mr. Freeze threatens to freeze all of Gotham City, he has a big snowglobe in his hand. He freezes the snowglobe, then shatters it in is hand. When he crushes it open with his hand, the inside of the snowglobe is empty. There is no water, frozen or unfrozen, that comes out of the snowglobe when it breaks.
Other mistake: This one is hard to describe. At the start of the movie, when Freeze and his gang are robbing the museum, Freeze looses his gun and it flies up to land on some sort of higher surface. However, it looks REALLY fake when it lands, perching right on the edge, which would be impossible for such a large weapon to do if thrown at that speed and from that angle.
Other mistake: Watch carefully during Freeze's opening heist: two of his goons accidentally check each other and nearly fall down. This can be seen on the left-hand side of the screen in the overhead shot (one skates next to Freeze, another skates around an ice spike) just as the camera passes a column. And where's that spotlight that follows Freeze coming from?