Anachronisms
Sections of the balcony at the Ryman Auditorium in Nashville, Tennessee were removed in 1993 after a major renovation to the facility. Prior to 1993, the balcony extended to the sides of the main stage. The early 1950s scenes at the Ryman in this film show the post-1993 layout of the facility.
At the Christmas party shown after Hank's first Grand Ole Opry performance you hear "Santa Baby", sung by Eartha Kitt, playing in the background. The song was released in October of 1953, around nine months after Hank Williams died.
When Hank reads a pulp magazine story to Lycrecia, the scene is happening in 1947, but the issue he is holding was published in November 1952.
Audio/visual unsynchronised
(At 00:24) As Audrey Williams is approaching the microphone in the radio studio you can clearly hear Hank say "She is slowly approaching the microscope" not "microphone".
Continuity
During the Universal newsreel segment, the copyright is MCMXL, which is 1940. It should probably be MCML, or 1950.
Glad someone noticed the year MCMXL (1940) on the Universal Newsreel - in that same newsreel, Connie Mack was being lauded in a parade for 50 years managing: that would have been 1936.