Factual error: Michael had his meeting withe Solozzo around Christmas of 1945. On the way to the meeting, the car made a U-turn on the George Washington Bridge (GWB) to throw off anybody who might be following. At the time, the GWB had four traffic lanes, two in either direction. The median between the two set of lanes was about 20 feet of steel mesh, making such a maneuver impossible. The median was filled in to add two additional traffic lanes in 1946. At that time, the u-turn would have been possible.
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.
Continuity mistake: When Michael is sitting with Sollozzo and McCluskey, the owner (presumed owner) of the restaurant (shown from the rear, walks behind the bar to ring up and put a check in the register, he is smoking a pipe. (in his mouth) But yet a split-second later from a front angle there is no pipe in his mouth, hand, or anywhere near him.
Other mistake: While Michael is talking with the Sicilian father, requesting to meet his daughter, the camera jostles twice, between the close shots of both men. (01:40:00 - 01:46:00)
Continuity mistake: When Woltz shows Tom Hagen his horse, Khartoum in the stables, the horse has a prominent white star on his head. The horse's head in Woltz's bed later that night has no such star, the head is all black.
Continuity mistake: When Tom is walking down the alley between buildings at Woltz Studios before he meets Mr. Woltz, the bag he is carrying looks like a travel bag and is almost equilateral triangle shaped. When he meets Mr, Woltz, his bag is a much thinner (isosceles triangle) shaped briefcase. In almost every shot the hand carrying the "bag" is switched. (00:27:45)
Continuity mistake: At the end of the shot where Al Neri shoots Emilio Barzini's bodyguards, the one on the right is still in the process of falling and hasn't hit the ground yet before it cuts, but in the next shot, he's already on the ground and not moving.
Other mistake: When Al Neri shoots Emilio Barzini's bodyguards, they're both only shot in the torso, but when they're on the ground, there's only blood coming out from under their heads.
Audio problem: When Vito Corleone is brought back from the hospital and he is upstairs in his bedroom with his other family members, after his grandson Frank gives him his gift, the baby who was just crying has his mouth completely closed while the audio has him still crying as they leave the room. (01:33:00)
Chosen answer: The mattress montage music is called "This Loneliness." It is written and performed by F.F.C's father.