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.
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.