Plot hole: The police wanted to take Julian's father away as a Jew because they found out his grandparents (plural) were Jewish. Even assuming they were only talking about one set of grandparents, this would make the father half Jewish, and therefore in the eyes of the Nazis, a Jew. That means that Julian would then be one quarter Jewish, and also considered a Jew. But the police then go on to say that the father is one quarter Jewish, but Julian is only one eighth Jewish, and therefore not a Jew. But he'd have to have only one Jewish great-grandparent to be non-Jewish, and they already confirmed that he had at least two. The numbers don't add up.
Factual error: In the scene where the resistance blow up a German train, the locomotive is a British one. The number is shown as 92240. This engine is owned by the Bluebell railway, who are named in the credits. It wasn't even built until around 1955. It seems to be the same engine pulling the train to the concentration camp later in the film. Remarkably fast repairers, those Nazis.