Factual error: Michael's impending 18th birthday is often mentioned as the time he becomes an adult and can make his own decisions. The age of majority in 1922 (and until 1970) was 21.
Other mistake: When Polly tells Ada about her two children being taken from her, she says Michael was 5 and "Sally" was 3. When she goes to the seance she says her daughter would be 18, but shortly after that Tommy finds Michael and he is 17. Also, when Tommy tells Polly that he found the records on her children, the daughter's name changes to "Anna."
Other mistake: The Birmingham police officer, Moss, is still listed in the credits as Sergeant Moss. He held that rank in Season 1, but in Season 2 he wears inspector's rank insignia. Campbell does address him as Mr Moss, the correct title for an inspector.
Continuity mistake: The first man to die in the ploughed field "execution" scene had the back of his head blown away by a gunshot. In the replay in next episode, his head shows no such effect.
Factual error: Major Campbell heads the Irish branch of the secret service, but reports to Winston Churchill, the Colonial Secretary. The Colonial Office had nothing to do with Ireland, which at that time was part of the United Kingdom.
