Continuity mistake: In the vault, just before Batman enters, we get a nice shot of the bank guard. He appears to be lying length-wise in the vault, his body flat and straight, and his head laying on the "step" toward the left side of the screen. When the scene cuts to Batman entering the vault, the guard is positioned differently, at much more of an angle, and his head is higher, closer to the second row of boxes from the bottom of the vault. (00:07:25)
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: In the part after The Riddler shows Two-Face the newspaper with the headline "Batman Survives Subway Sabotage," The Riddler pushes a glowing green cylinder into the monkey's mouth and the camera cuts to the screen so they can see Bruce Wayne's brain. When it cuts back to Two-Face and The Riddler, the cylinder isn't there. (01:25:54)
Visible crew/equipment: To escape Two-Face's ambush, Batman tilts the batmobile onto its rear wheels, and thanks to the bat-hook, he's able to use the vertical facade of a building as an alternate route. As the batmobile rides up the building, if you look closely you can see what looks to be a wire behind the batmobile (probably helping the batmobile or a model of it travel smoothly up the building or a model of the building). (00:50:35)
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.
Answer: It's called "Smash it up" by The Offspring.