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.
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.
Factual error: Bob finds the discarded animation cells of Woody Woodpecker, Buzz Buzzard, etc. at Columbia Studios (where La Bamba was produced). Actually, these Walter Lantz characters appeared in cartoons that were produced by Universal Studios.