Verdict:

I can see why. I can see why some people who watched the first 2 movies were severely disappointed after seeing this one.
Watching this third movie right after the first two felt like somebody had dug up bits and pieces of Godfather I and II at some archaeological site and then tried to create the third movie based on the style of the found artifacts. All the aging actors are now trying to remember whom they were playing in the original movies and the director is standing in the corner trying to remember how to direct and the writers got pens in their mouth and their eyes on the ceiling trying to remember how the previous movie ended and to somehow tie it into this new movie.
It is like a cow that was able to produce 2 good batches of milk, but now her udders are empty, and Hollywood is trying to squeeze yet another Godfather out them, but all you got are a few last squirts from a sore teat.
While the 2nd Godfather film had flown almost seamlessly out of the first, much about this third film is different. The tone has changed, with Al Pacino giving a much more subdued and humorous performance with those rising eyebrows that started dominating his later career. The people act contrary to their character types established by the first two movies. They try to make the gangster Michael Corleone into some sort of anti-hero in this one, which is missing the point of the series.
But at the same time, the creators expect you to have watched the first two movies, because right from the start there are references made to characters from the first two films without much explanation. The visuals are striking, but the gritty realism of the first two films is gone.
Al Pacino is still good at his role, but some of the other people are not. The world squarely put its crosshairs on Sofia Coppola as the scapegoat for this movie’s downfall, and I can see why. Maybe the problem is that English was not her native language or that she was playing a very different role than before, but this lady really phones in her performance. Something goes wrong in the intonation at the end of every sentence she utters. And it doesn’t help when the text she is given is so subpar.
In fact, the movie takes a number of dips in the quality of the dialogue. I got flashbacks of Star Wars prequels while listening to it. The screenplay is trying to be dramatic or poetic but often comes off as phoney. It’s not all bad though.
The story centres on one of Corleone relatives played by Andy Garcia and that guy is always good, especially in gangster roles, but you can’t expect him and the older Al Pacino to carry a Godfather film on their own.
The Godfather Part III has its good and its bad moments. It is unfortunately overshadowed by the greatness of its predecessors. If this was just a standalone film in a universe where Godfather I and II did not exist, I bet it would have been much better received. Therefore, the best I can suggest is to for the viewers to do the same as what the movies did: watch the first and the second movie and then wait a while. Watch the third movie a few weeks or even years later. That way the contrast will not be as startling.