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.
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: 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.
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).
Visible crew/equipment: In the scene where Vito shoots Fanucci, you can see the squib in Fanucci's waistcoat before it detonates.
Factual error: When Vito is about to kill Fanucci during a street festival, it is a cold winter's day. Fires are burning in 55 gallon drums along the street and Vito is wearing a heavy overcoat under which he conceals his shotgun. But the scene begins with the shot of a banner that reads "Festa Di San Rocco" which is August 16, i.e. in the summer.
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: When Michael meets Hyman Roth at his home in Florida, they sit in the room with the TV on. You can hear the football game being called by the commentator. The game is a USC/Notre Dame game with the teams called out by the commentator. The meeting takes place in the late '50's before Bautista's overthrow, but the game's commentator is Tom Kelly (very distinctive voice) who didn't begin calling USC games until the early '60's.