Seok-woo (the father) has consistently differing bloodstains on his shirt in different scenes (most notable after the multi-car trip to get back to the front). Also, the bloodstains appear very light on his shirt, like watercolors, rather than thick, dark, clotted blood.
In one scene, a window is clearly seen without any blood on it, yet in the next shot, from the inside, there are many blood stains on it.
At the 74-minute mark, when the passengers are trying to close the door and block the zombies from gaining access to their wagon, the door is almost closed, then half open, and then almost closed again.
For a train to travel to its destination over vast distances someone, usually an operator from a remote location, needs to keep the track switches on path. From what this movie depicts it is unlikely that the switch operator will stay intact long enough to make the train travel this far and still make it to its destination.
Everyone seems to be able to make and receive calls with ease. In reality, a national emergency with chaos on that level would surely cause the national cellphone network to overload, and that's ignoring the many cellphone masts that would be abandoned by technicians or overrun by zombie attacks.