Continuity mistake: When Gussie is telling Jeeves & Wooster that he gave the notebook to Sir Watkyn, in one shot, the scarf on Wooster's head changes from being wrapped around his neck to draped loosely on his head. In the next shot, it's back around his neck. (00:36:40)
Other mistake: When Tuppy goes to turn off the burglar alarm for Wooster, it's behind a hidden panel with a sign saying "Alarm Switch" above the panel. Why bother putting the switch behind a concealed panel if you're then going to label it? (Unless you're doing it for a viewing audience). (00:35:00)
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.
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)