When the main boy looks in the window at the North Pole and sees the record playing the Christmas song, it shows it to be a 45 rpm record. They were not invented at the time period of this move. 78 rpm was the standard wax record.
Know-It-All states that the train is a Baldwin 2-8-4 locomotive built in 1931. The Polar Express was modeled from plans of Pere Marquette 1225 which is a 2-8-4 type built by Lima Locomotive Works in 1941.
When the Hobo is talking to the Hero Boy about belief in Santa Claus, he tells him that he doesn't want to be led up the "primrose path," as if meaning that he does not want to be deceived. Being led up the "primrose path" denotes a life of luxury, while being led up the "garden path" suggests being purposely led astray.
When the Hero Boy is skiing with the Hobo atop the train, the camera angle pans several times. At one point, the view is from the front of the train, showing the engine and the two fellows are on the third car, with two cars between them and the engine. Subsequent pans show them jumping at least three more times, and traveling on more than just two cars.
Throughout the movie, the number of cars on the train changes, from just three, to as many as eleven plus. This is most obvious when the hobo and Boy are skiing on the roofs of the cars, and when they are on the ice tack.
Whenever the train is shown during the movie, all the cars' windows are fully lit from the inside. However, when the car containing the damaged and unwanted toys is shown in an interior shot, it is very dark and unlit.
The first time the Boy goes downstairs on Christmas eve there is a red snowman skirt on the tree. Then on Christmas morning, as the train is going around the tree the skirt on the tree is yellow kind of color and has bells on it.
When the conductor is punching the Hero Boy's ticket, you can see the holes flying out of the puncher and on to Hero Boy's face. If you count the holes that fell out against the holes that were punched on the ticket, they do not match. There are obviously more holes that fell out and on to the Hero Boy's face than were actually punched, most likely for effect.
Early in the film when Hero Boy is in his room, his robe is seen on the bedpost closest to the bedroom door - when his parents visit the room, that bedpost is bare, then when he goes to see the train, the robe is there again (and he rips the pocket).
After the caribou begin to step away from the track, the conductor instructs the train's engineer, "All ahead... slow." "All ahead" is an instruction appropriate for a ship with multiple engines but not for a train pulled by a single locomotive.
The hero boy has to jump between cars because of the gap between them. In actuality there are metal plates between cars to cover the couplers and allow easy access. When the conductor and the hero girl move from car to car they simply walk across.
The Engineer is commanded by the Conductor on the ice using "Left full!" and "Right full!" in order to steer it toward the tracks. In reality and as can be seen when the ticket is blown under the engine, the drive wheels of the locomotive are connected by thick, solid axles, which though they can move forward and backward, would not allow the train to turn left and right like the Polar Express was able to do.
Whenever the engineer opens the throttle on the locomotive, he pushes it away from him, the further away he pushes it the faster the train will go. In reality, the engineer must pull the throttle lever towards him to accelerate while pushing it away from him closes the throttle valve.
The moment the train crosses the Arctic Circle at 66 degrees and 33 minutes North it arrives at the "North Pole" which is located an additional 23.45 degrees north (A fairly lengthy distance). This is not important, as the place can be called North Pole with poetic license, as it's close enough.
When the elves are first seen, there is an elf that is moving (translating) left to right in front of the train with all the others, but the elf's body is rigid and lifeless, like a toy being slid across the floor. Possibly the computer animation for moving the elf from left to right was correct, but the algorithm for animating the body motion (walking, swinging arms, etc.) was stopped.
As the train is being pulled up the mountain with the track that curls around it tightly, just before the train enters the bridge that leads to the North Pole and as the Conductor is relating the story of the time he nearly fell off the train, the cars curve and bend to match the track as though they are made of rubber. This was done because the curve is much too tight for the cars to manage without scraping into the mountain.