The side stories are among the strengths (and weaknesses) of the novel. Here are my choices for best and worst side stories.
Best:

1. The Bocchiccio Family and how they helped bring Michael back from Sicily. This could have been a novella in its own right.
2. Neri, his background, and how he came into the Corleone Family. Another novella—perhaps a movie if fleshed out.
3. Luca Brasi’s background, as told to Michael by Filomena. Scary.
4. Vito’s rise and the gang war that he won (including how Luca handled the Capone gunmen).
5. Sonny and the boiler repairmen.

Worst:
1. Jules, Lucy and her operation. Puzo put us through an agonizingly boring and sappy interlude just so he could describe an operation that, probably, some friend or relative had, and that he couldn’t resist describing.
2. Everything about Nino.
3. All of Johnny Fontaine after Connie’s wedding.
4. Every bit of the Hollywood BS Puzo burdened us with. That Hollywood BS was what ruined “Last Don.”
Your views?

I'd say you pretty much hit the nail on the head with those. Neri's first visit with the Corleones is almost charming.

Not sure how much they qualify as side stories, but I liked Detective Phillips visit to question Kay and her "donnish" father. I also think Tom's back story provides useful background in how Vito earns people's allegiance.

I enjoyed the Neri backstory, particulalry since I read the novel after seeing the films. It helped to make sense why he had the police officer ruse down for the baptism hit.

And I agree on the Lucy Mancini surgery subplot. If I wanted to know anout freak surgery, I'd go watch TLC.

Like some others, I also read the book after first seeing the film. And after reading the background in the novel, it made Michael's return plausible. To me, it is a glaring omission from the film and one of my few criticisms of the storyline FFC utilized.

I think an interesting idea would have been to insert the Bocchiccio storyline as a flashback scene in GFII. They could have flashed back when Geary, Michael & Hagen were meeting to discuss the license. Within that scene, Michael gives Hagen a look implying that Hagen screwed up the information for the Geary meeting. It would have been interesting to show the viewer how instrumental Hagen had been to bring Michael home from Sicily even though Hagen was obviously in disfavor at the present time.

Not only does Michael return, but the timeline jumps forward a year and his face is fixed.

The side story about Lucy, especially the part about her operation, had me scratching my head the entire time. I kept reading thinking Puzo will eventually get to the point of why this story exists, but he didn't. Not only I felt my time was wasted with no refunds given, I pretty much got a bald spot from where I was scratching my head.

I agree. However, have any Board members ever read or heard Puzo's explanation for including the Lucy saga in his novel? If so, what is it.

I don't know, but I'll repeat my guess: Some female friend or relative of Puzo's had that procedure, Puzo interested himself in it, and stuck the Lucy/Jules saga in the novel just so he could describe it for his readers. It's the same reason he ruined "The Last Don" with all that Hollywood BS he learned during his years there.

Just a theory: you had a lot of doctor shows on TV then, and soap operas and true romance novels always doubled up on doctors and sex. Maybe the Lucy story was intended to sell some books to women?

Lucy Mancini's story and her fondness of Sonny's equipment kind of reminded me of this:

https://www.youtube.com/watch?v=J782jBp_pW0

Neri first, the Bocchicios second. 1) and 1a), if you will. The drop-off to third is too great to matter.

I agree with all your good side stories and what should have been in it.

I also agree the Lucy story about had me snoozing, and the talk about Luca shitting himself when they killed him didn't help either. He went a little "too deep" on some things. Johnny's story also had me pissed I had to read all of that.

I thought he was writing about himself the whole book.