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 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: 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: 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: 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.