Jeeves and Wooster is circa the 1920's and the Prohibition era, yet the marquees in the shots of Times Square show movies from the 1940's...The Outlaw with Jane Russell, and Saratoga Trunk with Gary Cooper.
When the glittery neon signs of New York City are shown, there is a Coca-Cola ad with the slogan "The Real Thing" prominently displayed. Coca-Cola has used this slogan many times over the years but the first time was during WWII - more than a decade after the series was supposed to take place. The sign also said "Coke" in some shots instead of Coca-Cola, another advertising slogan not used until years later.
At about the 36:58 minute mark as "Bertie" reaches the top of the house, one can clearly see the safety wire attached to "Bertie" in case of a misstep. It is also seen for a fraction of a second shortly before that as well. Neither "oops" takes away the effect of "Bertie" climbing up to the top floor of the mansion because he really did climb.
When Bertie is hanging from the awning, the burglar alarm can be heard ringing, but the hammer on the bell is not moving. When the shot changes to a close-up of the alarm bell as Bertie tries to silence it with his foot, the hammer is now moving.