During the song 'Lullaby in ragtime' Harry Guardino's cigarette slowly burns down but then, miraculously, becomes full length again.
As Red and Bobbie roll Dorothy onto her side after applying the hot wrappings onto her legs, we see the headline of the newspaper she was lying on stating that Hitler has taken Czechoslovakia. The Munich Pact, which gave Hitler Czechoslovakia, was signed in 1938. Dorothy was stricken with polio in 1942.
After Red and Willa have left the club and are traveling home, the cars seen through the rear window of the taxicab are distinctly 1940's to 1950's vehicles which were nonexistent in 1924.
During the 1940s World War II era sequences, designer Edith Head could not resist putting Barbara Bel Geddes, Tuesday Weld, and all the female members of Dorothy's birthday party in up-to-the-minute 1959 fashions which were unlike anything worn during the 1940s.
When Red leaves the club with Willa (after seeing Louis Armstrong the first time), he takes his cornet with him but has neglected to put it back in its case. Presumably because he was quite drunk.