Maybe it's just my imagination, but I feel like I'm seeing a lot more novels lately structured the way this one is. There are a lot of characters, scattered in time and place, each with his or her own story to be told, and they're tied together just tightly enough that the whole thing can be called a novel instead of a bunch of short stories. In general, I don't find it a terribly satisfying way to structure a book; I want to get lost in a story. That's A story. As in single. If I wanted to bounce from story to story, I'd be reading a collection of short stories.
With a book like this, every time I'm finally settling in and getting involved with one character, suddenly I'm whisked away to another that doesn't really have much in common beyond the moment of "oh, he's her daughter" that links the two.
And in Beautiful Ruins in particular, I had the added misfortune that my interest in each character was inversely proportional to Walter's. I'd have really enjoyed a novel about Claire, the put-upon assistant to an asshole Hollywood producer; or one about Pat, an aging pop has-been struggling with the realization that he probably never is going to be a star after all. But every time I'd just settled into either of their stories, Beautiful Ruins whisked me back to 1962 Italy and Pasquale, a sad sack innkeeper whose perpetual moping left me bored.
(And another thing that almost never works, and serves here to drag the Italy sections down: The addition of a real person as a character in a story otherwise made up of fictional ones. Richard Burton pops up here, and it's enormously distracting, not least because of Walter's authorial tic to always always always refer to him as "Richard Burton." Never "Richard" or "Burton" or "Dick," it's "Richard Burton this" and "Richard Burton" that. Lord, does that get old fast.)
If you like this style of storytelling, you may well enjoy the book. There was, after all, just enough of the interesting stories in it that I did finish, despite my lack of enthusiasm for the structure.