Welcome to the boards. Since you enjoyed the trilogy, I'd like to recommend that you read the original novel by Mario Puzo. You might also be interested in one of the cuts that show the films in chronological order (the flashback scenes from GF2 come first).

I may be wrong, but my impression is that most posters here consider GF3 to be "an entry to the series," along with the novel and the first two movies. It's a lesser entry than the other works, but still "canon" in a way other following works are not. I also think it's a common sense here that GF3 is overly criticized, because it doesn't match the standard of the first two films.

I happened to be in Washington during the Jordan years, and I think there is a common feeling between those seasons and GF3 - a sense of going through the motions. Coppola needed money, Jordan was looking for some new challenge, but in both instances there was a sense that the audience wasn't first in their minds.

Like Coppola, Jordan also had casting problems (see Kwame Brown) in his third act.