I'd just like to share two stories as told by Albert Goldman is his fascinating biography of John Lennon -- one general, one specific to this album.
First, Goldman tells how Yoko Ono was incapable of singing in tune or in time. Hence, this necessitated her recording innumerable takes of each of her songs, then leaving the producer to splice a usable "take" together, the logic being that she couldn't sing the same note off-key EVERY time!
In the second story Goldman explains how the strange programming of DOUBLE FANTASY came about. Basically Yoko Ono used to release her own solo albums at the same time Lennon released his because, as a publicity-monster (her only real talent) she felt that the attention garnered by Lennon for his projects would help her sales. Unfortunately for her, this never worked, and her albums never sold, regardless of when they were released.
So, for the DOUBLE FANTASY-project Ono talked Lennon into a sort of conceptual marriage "dialogue," where their songs would alternate with every track. It was a diabolically ingenious way of forcing people to listen to Yoko Ono songs, whether they wanted to or not!
I remember when this album came out and friends complained of having to stand by the stereo to listen to it so that they'd be able lift the turntable arm to skip over each Yoko Ono song as it came up. Fortunately, today we have programmable CD players!