"Waterfalls" was originally entitled, "I Need Love". Paul's house in Kent is called "Waterfalls," and the song was written before recording of the McCartney II album, and it shows. Outside of "Coming Up," it is by far the strongest song off of the mostly "experimental" McCartney II (1980).
As with the McCartney album of 10 years earlier, Paul played all of the instruments, except for Linda's backing vocals on the last song ("One of These Days"). McCartney recorded it without a mixing console, with all microphones plugged directly into the back of a 16 track tape machine. And in almost every case, Paul laid down backing tracks with bass, drums and guitar and added the vocals subsequently (technical info. from this site).
The relatively obscure video he made for "Waterfalls" shows what this recording setup could have looked like (at the beginning and end):