Factual error: Near the end of the movie, a DJ announces over the air that the crash had occurred that killed Buddy Holly, J.P. Richardson (commonly known as "The Big Bopper"), and Ritchie Valens. The DJ then plays the Santo & Johnny tune "Sleep Walk" as a tribute to the lost musicians. The crash occurred on Feb 3, 1959 (and one would assume the radio news announcement was within 24 hours of the crash). The song "Sleep Walk" was not released until July 1959.
Factual error: Buddy Holly is seen singing 'Cryin', Waitin' Hoping' at the Winter Dance Party. He hadn't actually finished composing this song, never mind recording it as a finished piece of work when he went on his final tour. This song comes from his final recordings 'The Apartment Sessions' which he recorded in New York and was finally released after his death, complete with added backing music and vocals.