At one point, Billie's agent tells her she will be the first jazz singer to perform at Carnegie Hall. But by the time she sang at Carnegie Hall, there had been many jazz performances there.
Some of the African-American male characters and extras sport modern (1972) hair styles with Afros or sideburns which were not in style in the 1930s.
The bottles of Miller and Budweiser beer are the modern (1972) style rather than the shorter bottles used in the 1930s.