Plot hole: When the police search the white car and the barn they fail to find the compartment in the car behind the boot in which the decoding equipment was hidden. This is completely improbable. It was a standard car, the compartment was not a secret add on, and the police were supposed to undertake a thorough search of everything.
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.
Plot hole: Danny receives the telegram from Rafe, telling him that he is alive, at the same time Rafe meets with Evelyn. The telegram must have been sent from Hawaii. Why didn't he just call on the phone? When Rafe reached the U.S. after leaving England why didn't he send a telegram then. In those days it took some time to travel from the Eastern U.S. all the way to Hawaii and there is no way he beat the telegram if it was sent when he returned to the U.S.