The main problem with portraying Jazz music on film is one of authenticity: is the film authentic to the spirit of Jazz music, including the life of Jazz musicians, the context in which they operated, and most importantly the specific music that they created.
There are four types of films: one is a straightforward audio-video recording of a Jazz concert, but in general we do not get much information about the life of the musician and the context in which they lived their music. The second is a fictional approach to Jazz, presenting the lead character as a Jazz musician, and telling a compelling story, for example the film ’Round Midnight by French director Bertrand Tavernier. The third is a fictional biography where the director takes liberties with the main character in order to tell an engaging story, for example Bird based on the life of Jazz legend Charlie Parker and directed by Clint Eastwood. The fourth is a straightforward documentary film, and there are many such documentaries on Jazz music, and the most ambitious is Jazz: A Film By Ken Burns, a 10 part documentary that is 19 hours long.