Continuity mistake: When the train arrives at the hero boy's house, the front engine is stopped directly in front of it. When the train is about to leave the front engine is stopped way far away in the distance. (00:09:30)
Continuity mistake: During the scene when the Polar Express slides across the ice and the conductor is telling the train controllers to head for the tracks, the distance between the train and the tracks keeps changing.
Continuity mistake: When the boy runs out of his house, as the train is arriving, they make a point of showing his footprints in the snow along with his sliding leaving long marks. However, when they pan back it is his footprints that are gone.
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.
Continuity mistake: Throughout the movie, the number of cars the train has changes. The scene where Hero Girl's ticket is surrounded by a pack of wolves shows the train having around 20 cars, but the scene where the train's on the ice shows it having 5.
Suggested correction: The entire journey is likely just a dream. There are many things in the movie that cannot happen in the "real" world, and the number of cars changing is just another aspect of the dreamlike nature of the trip.