Factual error: At the graduation carnival at the end of the movie, Danny enters wearing a letterman's sweater and explains to his buddies that he earned it by lettering in track. However, on his left sleeve are two stripes, indicating that he lettered in two separate years. Since you are only awarded a stripe for each year you letter, and since Danny was a senior when he lettered in track, his Rydell letterman's sweater should have had only one red stripe on his left arm.
Continuity mistake: During the slumber party at Frenchie's, when Rizzo brings out the wine, check out the junk on the headboard. Later in the scene when Marty is putting on her robe, the headboard is clear and now has a black fan on the left. Then even later when Jan says "You ain't getting your hands on my ears" the headboard is cluttered again, with the black fan too.
Continuity mistake: Sandy walks over to meet the girls after doing a cartwheel. On Sandy's cheerleading uniform, there is a LONG red string right next to the letter on her shirt. Then, suddenly, the string disappears in the very next shot. Then in the scene after that it is back again, and then the string is back on her shirt.
Continuity mistake: In the middle of the dance contest, Patty Simcox does a funny front walkover, and comes dancing towards the camera. Over her shoulder, you can see Sonny running up behind her. But suddenly it cuts to another angle, and Kenickie is running up behind her to lift up her dress, and Sonny is nowhere to be seen.
Continuity mistake: After Danny has danced around the car with the saran wrap he is shown spinning around numerous times, and then stops with his back to the camera. However, in the very next shot, his arms are suddenly up in a pose far too quickly for him to have done in the time alloted.
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Visible crew/equipment: In the scene during the American bandstand, at the end of the song when the teacher is dancing in front of the band members, the crews can be seen. The dressing and the hair doesn't match Grease era at all, and someone is sitting on a director's chair as well.