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.
Plot hole: When Ritchie appears at a pizza party sponsored by a local radio station, his manager Bob Keane is handing out copies of Ritchie's first album. In reality, the album had not been released until April 1959, two months after Ritchie's death. As the actual LP includes his biggest hit "Donna", Ritchie had not yet recorded (or even composed) the song in this part of the movie until a few scenes later.
Continuity mistake: In the scene when Bob takes Ritchie to "get laid", Bob approaches the girl in the pink dress at the end of the row, while Ritchie goes to play La Bamba. You see Ritchie play La Bamba and in the background Bob is all over that girl. The next shot cuts to Bob just arriving at the girl.
Continuity mistake: When Ritchie's brother lies down next to him in his bed, the covers are down to Ritchie's stomach whenever they show him in a solo shot, but are pulled up almost to his neck when the shot shows both brothers together. In the next solo shot of Ritchie, the covers are back near his stomach again.
Audio problem: Near the beginning of the movie there is a scene where Bob is talking to Connie and having the discussion about "honest" money. He grabs Connie's arm, hands her the wad of money and says "We're getting out of this s**thole tomorrow." But he is mouthing the words: "We're getting out of this *crap*hole tomorrow."
Continuity mistake: When Richie and his brother Bob get into a fight, Bob pulls on Richie's sweater and yanks his tie out of kilter. A few seconds later, Richie's tie is tucked in and his sweater is smoothed down, but not enough time has elapsed for him to have done this to himself. (01:00:34)