Factual error: The movie and events take place in 1958. However, two Fender amplifiers that are used by the band, "Johnny Casino and The Gamblers" are "Silverface" models that were only manufactured between 1967 and 1981.
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.
Factual error: When the Pink Ladies are walking Sandy into the outdoor cafeteria, just after she tells them the name of the boy she met last summer, all the cars in the background are from the 70's, not from the late 50's or early 60's. This actually happens twice in the same scene.
Factual error: In the scene where Danny is talking to Sandy at the Frosty Palace, the jukebox behind them is a 1973 model, but the film takes place in 1959.
Factual error: In the dancehall, the guitarist in the band is using a silverface Fender guitar amp. Fender did not manufacture this style till early-mid 60's. (02:00:00)
Answer: It is implied that Danny and Rizzo had a previous romantic relationship of some kind. When Jan says, "Did you guys get a look at Zuk this Morning? Looking pretty good this year, huh, Rizz?" Rizzo replies, "that's ancient history." Later, when Danny says, "you're looking good, Rizz, " her answer, "eat your heart out," also suggests some possible residual feelings on her part. I think that's why Rizzo enjoys tormenting Sandy and Danny by reintroducing them at Rydell at a moment that she knows Danny is going to save face around his friends.
Michael Albert