Factual error: The Cadillac Miller and Cadillac Meteor flower cars at Vito Corleone's funeral are an anachronistic impossibility, given that he died some time in the summer of 1955. With two exceptions (one from 1951 and one from 1955), the Cadillacs serving as flower cars are 1956 models. Although a 1956 Cadillac Fleetwood 75 limousine also makes an appearance, it's plausible that the funeral could be taking place at a time when the first 1956 Fleetwood 75's were released. Miller and Meteor, however, did not begin converting 1956 Cadillacs into flower cars until 1956 proper.
Continuity mistake: When Vito Corleone gets shot, he rolls on his back and his coat opens up to show his shirt. Then we see Fredo sitting down on the nearby steps and crying. In the next wide shot, Vito is lying on the side, totally covered by his coat, and Fredo is sitting farther away than where we saw him before.
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: 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: 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.
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: 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.
Factual error: In the establishing shot of the movie producer's mansion, a car in the driveway is suppose to be a 1937 Cord, but actually it is a replica produced between 1968 and 1972. Real Cord cars had bug eye headlights that cranked out of the fenders. The replicas had fixed glass covered headlights in the fenders.