Bowdlerise: The movie was originally rated "R" in the United States, but the studio re-released it to theaters in a "PG" version with little to no profanity, drug use, and nudity. Wikipedia has a picture◊ of the poster that advertised it.
Denny Dillon from Dream On and Saturday Night Live wants to wipe Tony's brow.
Hollywood Pudgy: Donna Pescow (Annette) gained 30 lbs to better fit the role, as well as training herself back to her Brooklyn accent. (Immediately after the film was done, she set to work losing the extra weight and the accent.)
The Red Stapler: As the main article say, the film created a nationwide craze for Disco music and Disco dancing (together with discotheques), while before Disco was mostly confined to the New York and Philadelphia gay communities. Also, Travolta's suit from the movie instantly became fashionable.
Very Loosely Based on a True Story: "Tribal Rites of the New Saturday Night", a 1975 New Yorker article. Ironically, it turns out that the article was completely fabricated.