Other mistake: When young Vito Corleone shoots Fanucci in the chest at the doorway to his apartment, in a continuous shot, a wound/blood bursts from Fanucci's white vest. When Fanucci proceeds to tear his vest open seemingly in disbelief he has been shot, there is no entry-wound, blood or hole in his white shirt directly under where the wound appeared in his vest.
Other mistake: When Paolo is shot dead, there's blood dripping down the rocks he's lying on, but there shouldn't be. The rocks are under his shoulder, and he was shot in the back, and a little blood dripped out sideways. And there's no blood on his shirt where his body is touching the rocks.