Continuity mistake: After the Hot Chocolate scene, the little girl takes a cup to the boy in the last car. When she leaves her seat, there is no ticket there, but the boy sees that she left it behind.
Continuity mistake: Nearing the end of the scene where the boy and hobo are jumping from the roof of one passenger car to the next on skis, the camera shot changes from a close-up to a distant view. In this distant view you can plainly see that they have just two more passenger cars to jump onto before hitting the coal hopper. However, when the camera returns back to a close-up shot, they jump three passenger cars before the boy hits the coal hopper.
Continuity mistake: After the kids reach the North Pole and they line up outside of the train, Hero Boy and Girl are at the back of the line and we can see the other kids in front of them. In the next few shots, they discuss helping the Lonely Boy. When the camera comes back to the same point of view of the boy and girl being in line, the rest of the kids have disappeared behind them.