Honoria Glossop Turns Up (or, Bridegroom Wanted!) - S4-E3
Factual error: Sir Roderick has moved his psychiatric clinic to New York because the BMA wouldn't approve of his methods. Although we don't get exact dates for the episodes, since prohibition was in effect in the last episode and Puttin' On The Ritz came out in 1929, we can presume it's the late 20s/early 30s. The AMA wouldn't recognize psychiatry as legitimate medicine until the 1940s. Sir Roderick wouldn't have had any better luck in America.
Lady Florence Craye Arrives in New York (or, the Once and Future Ex) - S4-E2
Character mistake: Cheesewright is trying to convince the police to raid the charity ball because alcohol is going to be served. The police chief tells him they stay out of private affairs and Cheesewright replies "The law's the law!" Prohibition made illegal the sale and transport of alcohol, but people were still allowed to have it in their homes or private functions. No laws were being broken. (00:33:30)