The name of the Kirward Derby (the legendary hat that makes its wearer the smartest person in the world) is a spoof on the name of TV host Durward Kirby, who was reportedly none too pleased by the honor, and considered suing the show.
Expecting to meet the U.S. President, Rocky suggests they give him the Kirward Derby (the magical intelligence-boosting hat they've been toting around), to which Bullwinkle replies, "I don't know if it'll fit over all that hair." Then-President John F. Kennedy was known for his full head of hair.