Other mistake: When Batman puts the lit torch to the cable and the cable breaks; the vault goes back into exactly the same place where the helicopter lifted it out from; connected via a grapple that Batman put through the wall. Ignoring the logistics of how this would be possible, it tightens the grapple, which surely, with the weight of the vault, would have ripped itself away from the wall.
Continuity mistake: In the beginning Batman suits up with a heavy leather-like cape. When he swings to the street his cape flaps and ruffles in the wind like thin silk; very obviously a completely different material.
Continuity mistake: When Bruce has just gotten shot by Two - Face and Riddler has just put the vowel riddle down, the riddle has a short stick with Bruce's head on the top to be a tennis ball. When they're taking Dr. Chase away, the bird's eye shot of Bruce laying shows no stick.
Other mistake: The headline of the newspaper says about Two Face robbing Nygma's party and Batman saving the guests, but the body of the text is about Thomas Wayne's death.
Continuity mistake: As the giant safe is being pulled out of the building, a large section of the wall above the hole breaks and starts falling outside the building. The shot cuts to outside and the hole is now back to the same size as before and no chunks of wall are falling. There aren't even any cracks where a piece might break off.
Continuity mistake: When the holographic floor disappears in Nygmatech, Batman is standing on a U-shaped "plank" extending out over the open pit. Cut camera angle to a shot looking up at him and he's jumping from a flat ledge; the U-shaped plank has disappeared.
Continuity mistake: When the Riddler blows up the Batmobile, if you look closely, you'll see its rear left wheel cap fell off at different angles.
Answer: It's called "Smash it up" by The Offspring.