The fascinating thing about this movie is that for every really bad thing there's a really good one to counter balance it: Sofia Coppola's amateurish performance (though she does look the part) vs Andy Garcia's electric one; Talia Shire's brilliant reinvention as a Lucretia Borgia type matriarch of the Corleones vs Diane Keaton's flat, permed Kay; George Hamilton's unexpectedly good turn as a lawyer vs wasting the role of Michael Corleone's son; some delightfully dodgy priests vs the insulting concept of the Mafia trying to save the life of the new Pope; the stunning production design vs editing which keeps chopping up scenes.
I disagree with Coppola's assertion in that the first two films told the story - there was much to be had from the saga of Michael Corleone's third act: the fate of him, the kids, his family, was inherently dramatic. And this film kind of has it - Michael wanting to go legitimate but being tempted back to the old ways; uncertainty over the loyalty of Vincent; worried about his kids and soul.
There are plenty of great moments and performances - the action sequences are done well, including an interesting assassination via helicopter through the roofs, and a revenge shooting at a parade; the finale was satisfying; support players like Hamilton, Eli Wallach, Mario Donatone (a genuinely scary assassin) and Joe Mantegna work well.
It does feel as though Coppola and Puzo could never quite get the drama right - it needed the extra conflict that would have been provided by Tom Hagen, or Michael's son, having a bigger role. Also the Vatican stuff, while kind of interesting, ultimately isn't that effective dramatically because it doesn't really involve the Corleones - it's not like the plan to take over Cuba in Part 2 where they had so much money involved - this is like a casual investment. Michael's son being an opera singer is dull. John Savage does nothing as a priest. I wish they'd just redone King Lear, which has a great structure for something like this. Still, it is worth watching.