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.
The Battle of Central Park - S3-E6
Character mistake: When Justine Feraldo looks at the checkpoint feeds, she says that the Strigoi have overrun the checkpoint at 116th Street and 110th and Amsterdam. But the feed says 118th and Amsterdam.
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.