Episode #1.1 - S1-E1
Other mistake: When detective Campbell is making his speech to the officers, the board behind him has dates ranging from 1966 - 1975.
Episode #2.3 - S2-E3
Other mistake: When the mother of a boy Arthur beats to death while boxing comes for revenge, she fires a single shot from a six-shot revolver at Arthur's head. Arthur then takes the revolver from her, ejecting 6 unspent bullets instead of 5. (00:28:24)
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.
Other mistake: There are multiple spelling mistakes in the sub-titles: Saltley is spelled Saltely, Balsall Heath is spelled Basall Heath, and Changretta in Italian would be Ciangretta.