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.
Continuity mistake: When they leave to kill Pauli it's light outside, when they are driving and Clemenza says that they to get more mattresses it's dark outside, when they stop to kill Pauli it's light again.
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.
Chosen answer: The mattress montage music is called "This Loneliness." It is written and performed by F.F.C's father.