Corrected entry: When Batman throws his first explosive on the speeding train, it hits the window and the glass breaks inward. It should break outward.
Correction: That's the physics of how glass windows break. Broken glass will move towards the direction it was hit from (that is to say if an object is moving towards the right when it hit the window, the glass will move to the left). If the window is broken from the inside, the pieces will fall inside. The only reason glass falls to the other side is because as it breaks and falls on top of itself, sometimes it's unbalanced and topples backwards.
Corrected entry: Before Alfred hits one of the bad guys in the front of the Wayne mansion, there are 2 guys, then just one.
Correction: Ducard tells the men "no one comes out, make sure" then we see two men walking toward the burning mansion. We don't know what they then did and it is reasonable they split up to cover different sides since there must be more than one way out. To get in the house, Alfred hits the one covering the entrance he uses, while the other man is simply someplace else. Not seeing the second man isn't a mistake.
Corrected entry: Bruce knows that Rachel was going to Arkham before his party, but he could not know that she was in the basement with Crane.
Continuity mistake: As Ducard is sliding down the ice toward the cliff, he's on his front, sliding feet first. Bruce is also on his stomach, but sliding head first. Then, just before Ducard goes over the edge, Bruce is instantly on his back, sliding sideways, right side toward Ducard, just in time to take Ducard's hand, saving him. (00:40:10)
Suggested correction: The shot from afar shows Bruce rolling as he grabs Ducard at the edge. He isn't instantly on his back.
The mistake is valid. In the shot from afar, Bruce is already on his back with no time to roll over into that position from the previous shot.
Correction: They're not explosives. They are small metal pieces, in the shape of a bat, that he also used earlier on in the film (to destroy the lights). The windows break "inwards" because of the speeding train causes wind to blow "inwards". Just like wind blows "inwards" when you pull down the windows while driving your car.
XIII