Film gets its acclaim from being the first big budget anti-hero movie,

Rating: 6/10 (16 July 2007)

To understand this films acclaim you have to understand censorship in America. Wikipedia has a nice section on the 'Production Code'. In short nothing remotely like this film was seen for decades. So when it was released it was a revelation for American movie audiences.
In todays light the film doesn't have the same impact it did back then. The script isn't written that well, the dialogue is labored and dull. Though Brando is amazing and deserved all the accolades he got from the film.
The plot is labored as well and drags in many parts. The enemies of the Corleone family aren't 3-d enough to really be too invested in the power struggles. In fact things don't really seem to be alive as in other mobster films like Goodfellas. The illusion of reality here isn't complete.
Godfather II is by far the tauter and better film, and the best in the series.