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.
Factual error: Inspector Rusk uses the term "trope" in its modern meaning of a theme or motif. This usage did not come into vogue until the late 20th century; the first such usage recorded by the OED was in 1975. The series is set in the 1890s and the language used is generally that of the time.
Factual error: Inspector Rusk lost an arm while serving in the army before he became a policeman. A one-armed man would never have been allowed to join the police in Victorian England - as today, all police officers had to join as uniformed constables and they had to be completely physically fit and able-bodied. Only the most senior officers (well above inspector) could join directly in a senior rank.