I have to go with 1968. What a wild year that was!
And very much "all over the place", too. While you had stuff like "Hush" by Deep Purple, "Sunshine Of Your Love" by Cream, and "Jumpin' Jack Flash" by the Rolling Stones in the top 5, and "Journey To The Center Of The Mind" by the Amboy Dukes in the top 20, not to mention Steppenwolf hitting their stride, the number 1 spot was often occupied by middle of the road-ers like Bobby Goldsboro, Herb Alpert, and Paul Mauriat. (Yes, "Hey Jude" was number 1 for almost 2 months, but 1968 was also the first year since '64 that the Stones didn't have a number 1 single in the US.) Likewise, in 1974, a year that a lot of hard rocking stuff was on the charts (BTO's hits "Let It Ride", "Takin' Care Of Business", and "You Ain't Seen Nothin' Yet", Golden Earring's "Radar Love", "Rock & Roll Hootchie Koo" by Rick Derringer, "Jet" by Paul McCartney), the number one song of the year was Barbra Streisand's "The Way We Were".