Plot hole: There are numerous problems with the final solution to putting out multiple burning floors of a skyscraper by blowing the water tanks under the roof. Blowing the floor under the tanks only channels the water into the Promanade Room. From there it cascades out the windows and - as we see in the film - falls to the ground without touching the fires on the lower floors. A tiny percentage makes it into the stairwell door and elevator shaft, despite the fact that the elevator doors were closed. All of the stairwell and elevator doors in the building were shut; none of this water makes it to the fire. Also, as we see the flames going out from all the floors no water is coming out of any of those windows, proving that the fires are going out without any water.
Plot hole: During Godfather I, when Michael was plotting the assassinations of the 5 family heads, he mentions to his father that his son Anthony is thee years old, and 'reading the funny papers.' In Godfather II, we begin at Anthony's first communion, and the date given is 1958. Yet, later at the party, Kay mentions to Michael that 7 years ago he promised the family would be completely legitimate. This was before they married and Anthony was born. (This promise was part of Michael's proposal to Kay.) 7 years ago would be 1951, so how could Anthony be 3 years old then? (00:10:40 - 00:32:20)