The Adventure of the Cheap Flat - S2-E7
Factual error: Agent Burt brushes off Poirot's question saying "When will you guys understand there is no such thing as the Mafia, the Black Hand or the Cosa Nostra?" The last term he uses, while not impossible (since members of the organization were indeed referring to it as such) is a huge improbability, considering that officially FBI (and certainly the general public Burt is lashing at) came to know the real name (adapted in "La cosa nostra") only decades later with the Valachi investigations. (00:24:05)