Only X-rated movie to win an Oscar for Best Picture:

Midnight Cowboy, 1969.
The X rating, coined by the MPAA in 1968, stood for "extreme" content and attached itself to a series of influential films before the term was hijacked by the pornography market, which produced features emblazoned with excessive (and unofficial) XXXs. ratings.
Source: Sacks, David. Letter Perfect. New York: Broadway Books, 2003., 1/1/2003

 
   
  Most Oscars won by a single film:

11
"Ben-Hur" (1959), "Titanic" (1997), and "The Lord of the Rings: Return of the King" (2003) have all won 11 Oscars.
Source: The Denver Post, 3/5/2006

 
   
  Only movie to have every member of its cast nominated for an Oscar:

Sleuth
The 1972 film's two cast members, Michael Caine and Laurence Olivier, both lost.
Source: Sunday Telegraph, 2/22/2004

 
   
  Actress who gave the shortest Oscar-winning performance in history:

Judi Dench
Dench's performance in 1998's Shakespeare in Love, for which she won Best Supporting Actress, was 8 minutes long.
Source: Toronto Star, 9/13/2004