UPDATE: My son John emails:
One of the Beatles books that's in the house---probably either Tell Me Why or Revolution in the Head--points out that near the end of When I'm 64, John plays some very idiomatic guitar, which seems to cause Paul to laugh audibly. So maybe John did like it.
And doesn't John do some nice harmony singing?
On the other hand, this is emailed by a reader:
Oddly enough, if my random-trivia books serve me as well as I hope they do, John wasn't a big fan of the song. It was, in fact, written by Paul when he was just a teenager, and was put on the album to honor is father (who, oddly enough, was indeed sixty-four years old at the time). The story goes that Paul's father never did like John, and this didn't make him like the song much more.
So, a mystery emerges. Email me if you have some answers.
ANOTHER UPDATE: I'm checking out the home library of Beatles books, and I see John's memory is right. "Revolution in the Head," footnote on page 176, has this to say about "When I'm 64":
Apart from backing vocals, Lennon contributes some anomalous folk-blues guitar picking to the final verse/chorus (2:17-2:29)--a style joke that provokes an audible grin from McCartney (2:23).
The same page of the book also says that "When I'm 64" was one of Paul's earliest songs and that it ended up on "Sgt. Pepper" because his father's turning 64 made him remember it.
Another emailer sends this link to a Playboy interview, with this quote from John, who was asked who wrote "When I'm 64":
Paul completely. I would never even dream of writing a song like that. There are some areas I never think about and that is one of them.
He may nevertheless have liked the song, but as indicated, it wasn't his sort of thing at all. I stick by my original opinion that "When I'm 64" should not be the name of a John Lennon art show.
YET ANOTHER UPDATE: Yet another emailer provides this:
Some years ago, I read a short story by sci-fi author Spider Robinson wherein, after Lennon was shot, his body was (secretly) put into (cryogenic?) storage of some kind. The punch line being [spoiler alert!] that, upon successful resuscitation / reanimation, he and Paul realize that they are both, indeed, sixty-four...
I like Spider's writing in general, and though this was a slight story, I guess it was sort of memorable! After brief Googling, it seems to have been "Rubber Soul" published in Omni magazine in 1984. It seems to have been reprinted in at least two short story collections, "Melancholy Elephants" and "By Any Other Name"... Check the sci-fi ghetto of your neighborhood library.