During the dance, Danny is shown dancing with Sandy and singing a portion of the song "Those Magic Changes." Sandy then says he's very good and that he should take singing up professionally. This is a reference to the fact that John Travolta played Doody on Broadway before going on to play Danny in the movie. (Doody sings "Those Magic Changes" in the stage version. The song was used as a dance number in the film).
In the stage shows before Grease was made into a film, Jeff Conaway, who plays Kenickie, played Danny and John Travolta played Sonny. Richard Gere also auditioned to play Danny in the movie, but John was given the part because of his role in 'Saturday Night Fever'. Also Didi Conn, who plays Frenchy, wanted to play Rizzo.
Singer Olivia Newton-John had hardly done any acting, and was terrified of the idea of starring in a big-budget musical. John Travolta (who was also a singer) was really supportive though, and sometimes when Newton-John made a mistake during filming, he would make it look like it was his fault and take the blame for it.
Stockard Channing was 34 when Grease was being made, and she was supposed to be playing a teenager. She was also the oldest of the main cast members.
Olivia Newton-John had to be sewn into her trousers at the end of the film as the zipper broke. They were put on in the morning and she was not allowed to take them off or go to the restroom while they were on, as the crew would have to waste time sewing them back on.