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.
Continuity mistake: When Tessio delivers the bulletproof vest and the fish, Sonny's hands are in one position (one below, one on top of the parcel), a fraction of a second later they are in a very different position (both on top, unwrapping). The parcel is half open while Tessio is carrying it but fully closed when he puts it on Sonny's lap.
Continuity mistake: When Don Vito Corleone gets shot, the camera angle from the side of the car shows Fredo bent over trying to pick up the gun he dropped, but when we see him from the camera angle from above, he's just walking to the front of the car. When the angle cuts back to the front of the car, Fredo is once again bent over trying to pick up the gun.
Continuity mistake: Before Paulie is shot, Clemenza gets out of the car to relieve himself and walks only a few steps away from the car. As Clemenza hears the gunshot, he looks back at the car to see Paulie slumped over the steering wheel, and the car is a much greater distance away, than just the few feet he had walked away from it. As Clemenza walks back to the car, it again takes him only a mere few steps.
Continuity mistake: When they're all deciding whether to wait until the Don is better before making a deal with Sollozzo, the cigar box is closed. The camera cuts away for a second, then back and Sonny closes the miraculously open box. He can't have opened it while the camera was elsewhere, because opening it would have taken the lid right past the camera.
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.