There are scenes where Billie Holiday strips naked and looks very emancipated though. But that is most likely because of the drug use, not an eating disorder
It is mentioned that Billie had been raped in the past. (Not shown onscreen though). Also there is a flashback scene where Billie's mother told her she would have to work in the brothel to make her own money. Billie is still a child, therefore she cannot legally consent. (Nothing physical is shown onscreen though).
There is a scene where Billie (after making a stop for a bathroom break) stumbles upon a family where one of the members has been lynched. Not too mention "Strange Fruit", one of her songs that is heavily featured in this movie is about lynchings.