The missing tooth and gum thing was a lie wasnt it?

It happened, but not at The Ed Sullivan Show. Buddy and The Crickets were touring the UK and before a show in Hammersmith, London Joe Mauldin knocked the caps off of Buddy's two front teeth during a scuffle. Buddy repaired the damage with chewing gum and performed the second show with the gum spread over his front teeth.

Unmentioned in the film is that Buddy and the Crickets toured the UK a few times and were very popular in England (even more popular than they were in the US). Paul McCartney has said they were a major influence for the Johnny and the Moondogs and the Quarrymen, early incarnations of the Beatles. The name The Beatles is a reference to the Crickets, with the spelling changed for the "beat" generation.