Factual error: Sir Malcolm tells Vanessa to wear a facemask when they go to minister to the poor as cholera is rife in the area. However, the series is set in the 1890s and it had been well-known since the 1850s that cholera was caused by contaminated food and water and not by airborne germs. As an educated man, Sir Malcolm is bound to know this.
Occultation - S1-E6
Factual error: Eichhorst seems to be unsure what his SS rank is. He is addressed as Standartenführer (Colonel) but wears the epaulettes of an Obersturmbannführer (Lieutenant-Colonel) and the collar patch of a Sturmbannführer (Major). In addition, his other collar patch bears the standard SS lightning runes instead of the death's head of the Totenkopf concentration camp personnel.
Factual error: Constantine's driving licence is shown - it's a UK licence, but no. 7 where his signature should be is blank, and no. 8 where his full address should be simply says "England, United Kingdom." Both are printed onto the licence when it's issued - without that info it would never be issued in the first place. And it's not a fake, because why would he have a fake licence with his real information on it? It's just an incomplete prop.