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: 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.