Continuity
The bruise on Tanya's eye disappears and reappears between scenes.
Incorrectly regarded as goofs
Wilford congratulates Curtis for being the first human being to walk the whole length of the train; however, Claude, Wilford's assistant, is seen at the tail of the train, as well as the front. Though Claude does not travel very far into the tail section and while she has been in ever car, Curtis has been to the very back of the train, making him the only person to traverse its entire length. The children taken by Claude, however, were the first people to travel along the entire length of the train.
Continuity
During the shootout scene with the security guard they aren't on the right train cars. Curtis is shown on a train car towards the front of the train before the shootout scene takes place. If security was just shown killing the rebel forces who stayed behind, then they should be on a train car towards the back. Instead Curtis was firing on an upwards angle which should not have been the case. He should have been shown firing at a downward angle.
Errors made by characters
At the end of the film, Curtis reveals that he killed Edgar's mother when he was still a baby. Presumably, Edgar is raised by Curtis, Gilliam and others in the back of the train. Edgar has a very strong Irish accent and yet, there doesn't appear to be any other Irish people around. If he was raised on the train since infancy, his accent should reflect those around him, the majority of which are American.
Plot holes
Some children are taken away from the back of the train, and it is learned later from Wilford that small children are taken because they are the only ones that can fit into the sections of the engine that need repairs. This has been going on for years, yet the parents and others act as if this has never happened before.
Warning: Spoilers
Goofs below here contain information that may give away important plot points. You may not want to read any further if you've not already seen this title.