At the end of the film, Curtis reveals that he killed Edgar's mother when he was still a baby. Presumably Edgar was raised by Curtis, Gilliam and the others in the back of the train. Edgar has a strong Irish accent even though there don't appear to be any other Irish people. If he was raised on the train since infancy, his accent should reflect those around him, the majority of whom are American or English.
There is scene where Curtis realizes that the protein bars are made from insects and he acts completely disgusted. Yet toward the end of the film, he reveals that during the beginning of the train journey, he and others in the back of the train began eating other humans (including babies). It doesn't seem to make sense that he would be so disgusted at the thought of eating protein bars made from insects if he had once eaten babies to survive.
When Namgoon smokes his 1st of the 2 remaining cigarettes he lights it with 1 of the 2 matches. Then small boy steals the matches from his hand. Later when Namgoon offers Curtis the last cigarette the matches are back in the box and there are again 2 matches.
When Wilford is discussing with Curtis that taking over command of the engine is Curtis' "destiny", the shot overlooks the entire train car where Curtis, Wilford and Claude were previously sitting. In this shot, Claude is nowhere to be seen, but she later returns to the shot, inside of the car, when Yona opens it from the outside.
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.
During the scene of the shootout across the gap between Curtis and Franco the Elder, the last shots they take at each other are not only stopped by the intended target's window, they actually become stuck said windows. Curtis' firearm is a submachine gun, using pistol cartridges (probably 9mm), while Franco's is an assault rifle, most likely using NATO 5.56 (or .223 civilian version) rifle cartridges. Therefor, Curtis' shot probably wouldn't even have made it across the gap to hit Franco's window (nor during the preceding shots), while Franco's shot would have certainly penetrated Curtis' window and hit him. Pistol cartridges have a very short range and much lower power and velocity in comparison to rifle cartridges. Even further, Franco would have had to be an extremely good shot to gauge the lead needed to accurately target Curtis because of the moving target, and it's doubtful that they had regular target practice sessions on the train, let alone targeting moving objects.
The opening captions state: "Soon after dispersing CW-7 the world froze all life became extinct." but then a few moment late it follows that caption with: "The precious few who boarded the rattling ark are humanity's last survivors"
If humanity had any survivors whatsoever, then by the definition of 'extinct' all life DIDN'T become extinct.
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 every 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.
Wilford as well as Mason performed one specific hand movement (Wilford at the end of the movie, Mason during her speech to the tail section inhabitants) that suggests, that both of them have experience with cleaning the engine (as seen on Tim under the floor tile). This does not make any sense with regard to their age as the engine can be cleaned only by children less than 5 years old (the train didn't even exist, when both of them were 5 years old).
The goof item below may give away important plot points.
After the explosion and derailment there is a shot with fire inside of a derailed and tilted train car. The direction of the flames and the path of a falling object prove a tilted camera rather than a tilted train car.