Visible crew/equipment: After the first scene showing the plane starting up its engines and turning around, we are shown another scene of rioters throwing slot machines out of a club. In the bottom centre of the screen you can see a silhouette of what looks to be a part of a jigsaw puzzle piece on the camera. The object must be on the camera because when the camera pans to the right and down, the silhouette stays in the same position in the picture. (01:42:05)
Other mistake: When young Vito Corleone shoots Fanucci in the chest at the doorway to his apartment, in a continuous shot, a wound/blood bursts from Fanucci's white vest. When Fanucci proceeds to tear his vest open seemingly in disbelief he has been shot, there is no entry-wound, blood or hole in his white shirt directly under where the wound appeared in his vest.
Factual error: When Michael meets with Hyman Roth at his home in Florida the television is on and you can hear the announcer calling a USC/Notre Dame game. The meeting takes place in the late 1950's. The announcer's voice belongs to Tom Kelly, a long time USC announcer, but he didn't start calling their games until the 1960's.
Factual error: At the New Year's party, when everybody is running out from the goverment's palace, you see the flags at the entrance are from Cuba, but the coat of arms is from Dominican Republic (the country where this scene was filmed). (01:40:45)
Continuity mistake: In the scene where Roth's symbolic birthday cake is divided among his partners, we see a shot in which Michael is seen, in long-shot, putting a forkful of cake into his mouth while talking about the rebels. The thing is, it does not sound as if he is talking through a mouthful of cake. What is more, when the scene cuts to closeup, he is not chewing anything, even though it's just seconds later.
Visible crew/equipment: In the scene where Vito shoots Fanucci, you can see the squib in Fanucci's waistcoat before it detonates.
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)