Audio problem: During "We Go Together" at the end, John Travolta's mouth is not in sync with the words "we'll always be like one." He appears to start singing "that's the way it should be" before realizing and correcting his mistake.
Audio problem: At the cotton candy stand at the graduation carnival, Blanche is seen silently mouthing the question "How many?" In the next scene, from a different camera angle, the same question is asked - this time with audio intact.
Audio problem: When Johnny Casino & the Gamblers perform "Hound Dog" at the National Dance Off, you can hear the song, but if you look carefully you can see it does not match the lead singer's lips.
Audio problem: When Sonny says "Shut up!" to Putzie outside Kenickie's car, his mouth doesn't move.
Audio problem: At the very beginning when they are singing "Summer Loving" Sandy sat at the top of the seating for the athletics track. The voice-over and Sandy's lip movements do not match.
Answer: Watched that scene again now and I just think it was poor writing (in what's still a classic film regardless). How none of the judges noticed that Cha Cha took another girl's (Sandy's) place even after she'd already been "tapped out" is another huge plot hole. Plus a lot of people in America were watching the dance on TV and it's not mentioned by anyone after this scene. 35 years later and that scene still bugs me (haha).