My favorite subject for any movie set in this era - Correct music. Lots of people will correct errors in the costumes, or in historical events (which as near as I remember were all presented correctly) but the music is another matter.
BILLIE HOLIDAY WAS NOT THE ONLY PERSON MAKING RECORDS IN THE EARLY THIRTIES. They even did this in Schindlers List - the only American record played in the entire movie is in the opening scene, and its a damn Billie Holiday record.
ALL of the club music was wrong, as in seriously wrong. I'm guessing correct music would have been too distracting.
Other than that, this movie just dragged. There was no need for it to be this long.