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)
Factual error: When Michael arrives at Hyman Roth's house you can see the 1974 State of Florida green inspection sticker on Michael's car. The movie's supposed to be in the late 50's. (00:59:00)
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 weapon. 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: In the scene of young Vito Corleone coming to America, his ship passes the Statue of Liberty going the wrong way, south, whereas the docks of Manhattan, where immigrants were dropped before being ferried to Ellis Island, are to the north. (00:06:55)
Factual error: When an adult Vito returns to Sicily, and visits Don Ciccio to take his revenge, the sea can be seen over his shoulder. There is no sea anywhere near Corleone, Sicily.
Factual error: After the attempted murder of Frank Pentagalli takes place, as the shootout in the street continues a Mark II Jaguar is parked across the street. Not in 1958.
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, but the announcer is Tom Kelly, a long time USC announcer who didn't start calling their games until the 1960's.
Suggested correction: The announcer calls out Don Buford and Luther Hayes. These players were on USC's roster together only in 1958. Therefore, the game must be the 1958 matchup that Notre Dame won 20-13. This is not a factual error.
The announcer has the voice of Tom Kelly, who did not announce USC games until the early '60's.
The point is that given the announcer heard is calling a real game from 1958, it's almost certainly the actual announcer from that game. There'd be no point in hiring Tom Kelly to call a fake game. The announcer must just sound like him, but be someone else. Tom Kelly isn't in the credits, which he would be if he was specifically cast in that role.
Factual error: Corleone and Roth meet in Havana in Christmas 1958. The initial scene shows a panorama of a full street with people and American cars passing by. Among the cars we see a Jaguar Mk.2 in the opposite lane driving away. New Years day 1959 Batista flees the country and Fidel Castro takes over. The Jaguar Mk 2 wasn't introduced until late 1959.
Factual error: When Fredo arrives at the hotel to meet Michael in Havana, the flag at the entrance is from the Dominican Republic, not Cuba.
Factual error: When a rebel sets off a grenade killing himself and a captain, you can see some soldiers carrying FN FAL assault rifles. Batista's army didn't have those. They used M1 Garand carbines and rifles as main infantry personal weapons. Barista's armed forced used legitimately supplied US ordinance and they did not need or use black market European weapons.