Not even close to the first two, but probably not as bad as you've heard. I recently picked up The Godfather DVD Collection, having seen (and loved) the first two films. I proceeded to watch the first two over again, enjoying every minute almost as much as the first time around. Then I watched the third one, which I had never seen before. I'd heard how bad it was, and how Coppola ruined the series with Part III, so my hopes were less than high, even though the brilliance of the first two films was still fresh in my mind. So I watched it all the way through, trying to keep an unbiased oppinion.
Well, it's not great, that's for sure. But I wouldn't call it horrible either. It certainly lacks the wonderful mood and appeal of the first two films, and it doesn't hold together nearly as well. The first two are so masterful that it takes a very keen eye and many repeated viewings to find even the most minute flaws in them. In Part III, there's plenty of cheesy scenes, forced acting and hammy lines. On the other hand, a lot of the scenes were really good. I liked most of the time spent in Rome, especially the confession scene with Michael and the soon-to-be Pope. The construction of the story itself was pretty decent as well, although it's ruined a little bit by some bad acting.
The main problem with the story of Part III was that it wasn't about anything the audience really cared about, and it certainly wasn't anything new. Part I gave us the story of an aging Mafia crime boss, who's family goes into chaos when he's shot. And Michael, the moral son who doesn't want to get involved with his families business, but feels it's his duty when he sees the corruption in the law and the government. Part II gave us the continuing story of Michael Corleone, trying to vanquish his enemies, and it also had the side story of Vito Corleone as a young man coming to America and his rise to power. To me the scenes with De Niro as Vito was the best part of Part II, and I don't think the film would've been nearly as great without them. Part III was the story of the aging Michael Corleone, but we'd already seen the same type of thing in Part I. So we start looking for parallels between Parts I and III, but they're just not there. So we start looking for originality and redeeming qualities of Part III on it's own, but we have a hard time looking past some of the flaws.
Frankly I just didn't really give a damn about any of the characters in Part III. Michael was an old man, and I could guess he would be dead by the end of the film. Connie had suddenly turned into this hard Mafia consultant, which didn't seem to fit her character from the originals at all. Vincent was basically James Caan's character, Sonny, from the original, only Andy Garcia isn't as good an actor and didn't pull it off as believably. Also it seems hard to believe that Michael would leave the family in the hands of someone so brash and forward as Vincent. The character we were really supposed to care about, Mary, was completely blown by a terrible acting performance by Sofia Coppola, that has to be one of the worst casting calls I've ever seen. I literally laughed at the end (you all know what scene I'm talking about), her acting was just so canned and cheesy it was really pathetic.
On an up note, the cinematography was great once again. Although the film didn't have the same play on light and shadowing that the first two had, it did have some amazing shots of Rome and Sicily. The film was very pleasent to look at throughout. The music was also very good, although I think they used Nino Rota's original theme a bit too much.
Of course, if you compare Part III to the first two films, your going to come up with tons of problems with it and probably won't like it very much. But on it's own it's a pretty decent movie, there have been tons of better Mafia films (Goodfellas, Casino, Donnie Brasco etc..) but it's still alright. What's so disappointing is that the first two are amazing, and the third one is just pretty good. But it says a lot about a series when the worst of the bunch is still a good movie. On a scale of 1 to 10, I give The Godfather Part III, 6 stars.