Factual error: Fredo is wearing a very 1970's sport coat and wing-tipped shirt ensemble in the Las Vegas hotel scene, set some 20 years earlier.
Continuity mistake: When Michael Corleone goes to Las Vegas to meet with Moe Greene, watch carefully when Moe sits at the table while continuing his argument with Michael. There's a glass of water that changes places from shot to shot. At one moment, the glass is behind Moe's arm, then in the next shot it's in front. Moe moves the glass at one point, but nevertheless, the glass continues to move from shot to shot.
Factual error: At the end of the movie, when Michael's car is parked in front of the Las Vegas hotel, if you look through the glass windows, you can see two men with 1970's "hippie-style" haircuts walking through the hotel lobby. This is supposed to be in the late 40's or early 50's.
Continuity mistake: When the baker is meeting with Don Corleone about keeping Enzo in the country, he's holding a shot glass in one hand, and a thin cigar in the other. When he reaches out to clasp the Don's hands in gratitude, the items are gone. A split second later, they're back.
Factual error: On the way to the meeting when Michael is going to kill Solozzo, the car made a U-turn on the George Washington Bridge (GWB), which connects Manhattan to New Jersey. However, the scene is shot on the Queensborough (59th Street) Bridge, which connects Manhattan to Queens. They look nothing alike, the GWB is a suspension bridge, the Queensborough Bridge is a cantilever bridge.
Continuity mistake: In the meeting of the heads of all families, when Tattaglia asks the Godfather for assurance that there will be no vengeance, we see him leaning back in his chair, waiting for an answer. In the next shot the camera is on the Godfather, and we see Tattaglia leaning back again.
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.
Revealing mistake: When Michael calls Sonny, after he finds out that his father has been shot, the phone booth he calls from has a broken dial - you can see that the dial is off center and would not work in that condition.
Continuity mistake: At the restaurant, Michael, Sollozzo, and Captain McCluskey have just sat down at the table and the waiter comes over to take their order and pour wine. Sollozzo recommends that McCluskey try the veal, but McCluskey is already eating his dinner. By the way he is using his knife and fork, it is obvious that he is eating an entree, not a salad or an appetizer, even though they just arrived.
Revealing mistake: When Michael is riding in the car with Sollozzo before the assassination, notice the headlights in the rear window during the close-up. You can notice that many of them move directly on top and underneath each other, impossible for real car's headlights to do such a thing.
Continuity mistake: Outside the hospital McCluskey punches Michael. A few days after the episode outside the hospital, Michael shoots McCluskey and Sollozzo at the restaurant, but there is no mark on his chin where he was hit. Then at Sicily when Michael for the first time meets Apollonia, there is still no mark on his chin, but suddenly at Apollonia and Michael's wedding, he has a LARGE mark on his chin.
Factual error: When Luca Brasi goes to meet the Tattaglia family and Sollozzo to pretend he would like to defect, and they garrote him, Brasi is making all kinds of loud noises while being strangled until he dies. During choking or strangulation, one is unable to make much (if any) sound because air cannot pass through the vocal chords on its way out of the body just as it cannot enter the body and get to the lungs.