Trivia: The infant playing Connie and Carlo's baby son Michael Francis Rizzi who Kay holds during the christening scene is Sofia Coppola, Francis Ford Coppola's daughter, who was born in May 1971. Sofia later had a prominent role in Part III as Michael's daughter, Mary. Other than the main characters, Sofia is the only actor to have appeared in all three films. In The Godfather II, she can be briefly seen as an immigrant girl on the ship that brings Vito Corleone to Ellis Island.
Continuity mistake: When Luca Brasi is practicing his speech he is wearing a square faced watch. When he gives his speech to the godfather he's wearing a round faced watch.
Continuity mistake: When Sonny is shot at the toll booth the front windshield is torn apart by bullets yet when the bodyguards arrive thirty seconds later, the windshield is intact. (01:53:20)
Continuity mistake: After Michael shoots Sollozzo in the head, he turns to McCluskey and shoots him in the throat and then in the head. But in the long shot, before he shoots McCluskey in the head, you already can see the hole in the forehead. (01:25:15)
Revealing mistake: When Moe Greene is shot through his right eye, the eyeglass is cracked, but has no hole where the bullet penetrated the glass. (02:33:50)
Continuity mistake: When they're all having a meal in Sicily, watch behind Appollonia. Two people, one in red, one in white, walk past in the same direction twice - once in a wide shot, and once in a close-up of Appollonia. (01:40:35)
Continuity mistake: When Michael and Kay are eating lasagna during the wedding, Kay is smoking a cigarette. But depending on the shot, that cigarette disappears from her hand, then reappears. (00:13:25)
Continuity mistake: When Diane Keaton and Al Pacino have dinner, he gets up, puts on his coat and sits down again. Now watch Diane Keaton's glass: When the camera's on Al Pacino she's holding the stem, but when the camera's on her she's holding the body of the glass. Another mistake is that at the end of the scene the amount of wine in her glass suddenly doubles. (00:58:00)
Continuity mistake: When Marlon Brando is gunned down at the fruit stand, he drops the bag of fruit he just bought. However, when he's collapsing against the car, the bag of fruit is now on the hood of the car. (00:43:05)
Continuity mistake: When Clemenza knocks at the door Sonny gets a gun from a drawer and puts it in his belt. When he pushes Clemenza the gun disappears, but it's back a moment later. As the shot where the gun disappears is uncut the gun must have slipped down his pants. (00:46:20)
Visible crew/equipment: After Paulie gets shot there's a reflection of a cameraman in the small triangular side window of the car. (00:55:10)
Continuity mistake: In the first scene, the undertaker Bonasera asks the Godfather for help. When the Godfather gets up from his desk, the rose in his lapel is either fresh and straight or slightly wilted and bent in alternating shots. Also, later in the wedding scene, this rose keeps recovering from intermittent spells of withering. (00:06:00)
Suggested correction: Look again, the broken windows you are seeing are from the side windows, the windscreen was shot out entirely.
The screenshot shows the windscreen is intact after being shot out.