When we see Gene at his penthouse on Central Park, at the party one of the guests is Bix Beiderbecke. Bix died in 1931 and only ever played with Gene Krupa in Chicago. By the time Krupa made it in New York, Bix had already died.
In the scene between Gene and Ethel, right after Gene's mother argues with him in the speakeasy about the priesthood, Ethel's small handbag on the table is closer to her on the close-in shots than it is on the longer shots.
In the final scene, when Krupa makes his comeback appearance with Tommy Dorsey's band, the set he's playing changes in the close-ups from the front left. The high hat cymbals are in a different position, and the tom tom to his left disappears completely.