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.
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.
Audio problem: When Ritchie is playing in the country bar, Bob's drumming is inconsistent with the drum sounds.
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.
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.
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.
Continuity mistake: When Ritchie is driving, it shows the speedometer at 80 mph, but in the wider shot he's obviously going much slower. You can tell by how fast the lines on the street are going past.
Continuity mistake: When Donna and Ritchie are riding in Donna's convertible they're going relatively fast, but Donna's hair is hardly blowing at all.
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."
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.
Continuity mistake: When Richie is showing the new house to his mom, Bob on his car says OK, lifting his hand, but in the next shot his hand is down.
Factual error: It said the Big Bopper was 29 when he died. Actually, he was 28 when he was killed.
Character mistake: The bulletin of the plane crash announces J.P. Richardson (The Big Bopper) as from Louisiana. Richardson was born in Sabine Pass, Texas and later moved to Beaumont, Texas where he lived for the rest of his life.
Other mistake: Ritchie's 1950's Fender guitar amp looks like it would have looked in the 1980's when it should have only been a couple of years old in the movie.
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.
Continuity mistake: At the bar in TJ Ritchie gets to the stage to hear the song, but in the next shot he is a few feet away.
Continuity mistake: While Ritchie speaks with Rudy about his audition, Rudy has an empty bottle of coke but in the next shot the bottle is full back again.
Continuity mistake: After Ritchie has a gig at the cowboy bar, he is taking breakfast at home and the amount of food on his plate increases and spreads out.