Continuity mistake: About 3/4 through the film, which is supposedly set in the 1900s, there's an exterior shot of Jenny Agutter (as Roberta) talking to William Mervyn (as "the old gentleman"). Over Mervyn's shoulder can be seen a white delivery van driving rather fast along a road on the other side of the valley from where the filming took place (this is very obvious in the wide-screen version but less noticeable in the pan-and-scan TV version).
Continuity mistake: In the scene when the Grammar School boys are on the paper chase they run through a railway tunnel. The Railway Children go to the opposite end to see the grammar school boys come out, as they are waiting for the final boy to come through, the paper that is thrown on the floor for the boys to chase appears then disappears several times.
Revealing mistake: In the scene where the children are stopping the train with the red petticoats, just before the train has completely halted, you can see the reverse effect used in the film. The train is actually reversing away from them for safety, and when reversed, the red petticoats are swaying with unnatural movements as they're being waved by the children.
Plot hole: It is clear that the tunnel through which the paper chase leads is straight and level. Anyone running from one end to the other will get there quickest by this route. However the three children confidently predict that by climbing up a hill and back down the other side they will get to the other end first, and succeed. This would not happen.