Factual error: There are many instances in this movie where ice is doing things that ice doesn't do in the real world. Examples include Mr. Freeze freezing the pipes to make a hole in the wall, ice making things crumble all of a sudden, or something shattering easily just because a vehicle drives through something that is covered in ice.
Plot hole: After Freeze blasts Robin with his cold ray he just picks the diamond out of his hand with no problem. Why didn't the diamond freeze along with Robin?
Revealing mistake: In one scene where our heroes are defrosting Gotham city using the sunlight, we see Commissioner Gordon stepping from his car which has been covered in flexible icicles.
Factual error: If everyone had been frozen for that length of time, their blood would crystallise, which would kill them. I imagine some of the buildings and anything made of glass might crack as well, but I don't really know about that.
Continuity mistake: When Bruce and Julie go to the party in the observatory and are swamped by people, in the overhead shot at the start of the scene we can see that Gossip Gerty is trying to get to Bruce and Julie and that there is a man between Gerty and Julie. However, in the next shot (a tighter shot of the couple and onlookers), Gerty is suddenly right next to Julie, in the place where the man had been, with no time for him to move.
Continuity mistake: In the last fight against Bane, Bane has got Robin and Batgirl by their throats against an icy wall. In a close-up of Batgirl, Batgirl's right hand is near Bane's spiked wrist guard. However, in the very next shot, her right hand is more near Bane's elbow.