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.
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: 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.
Factual error: The calendar in Ritchie Valens' mother's kitchen is wrong. The calendar is open on October 1957. That year Oct 1 was a Tuesday and the movie calendar has it as a Wednesday.
Factual error: As Ritchie and Donna go for a drive, the middle of the road has double yellow lines which did not exist in the 50's - all road markings were white until the early 60's.
Factual error: It said the Big Bopper was 29 when he died. Actually, he was 28 when he was killed.
Factual error: When Ritchie is at the Winter Party Dance Tour, he calls his producer and then calls Bob, and puts a coin into the pay phone. The problem is that he was in Iowa, and they were both in California. Making a toll call to California would have cost a lot more than that one coin.