Revealing mistake: After The Russian smashes The Punisher's refrigerator door against his head a couple times, he shoves The Punisher to the floor and pushes the refrigerator door shut, but the refrigerator door suddenly and completely stops moving midway before closing, revealing the door to have a stopper built in so as to not actually hit the actor in the head with it (acknowledged by the director in the film's commentary track).
Continuity mistake: When Frank reveals himself to the public in front of a group of reporters and two former co-workers - when we first see him, you can see he is wearing a black button-up shirt that is buttoned all the way up, except for the top two, revealing that he is wearing his skull t-shirt underneath. (You can see the top of the skull peaking out.) But a few shots later, the bottom half of the shirt is completely unbuttoned (only one button is actually buttoned up), with him having no time or reason to do so between shots. In addition, when the bottom half half of the shirt is unbuttoned, you should be able to see the rest of the skull, but you can't. You can tell the skull just sort of stops midway down the shirt, revealing that he is wearing an alternate version of the t-shirt that only had the top half printed on it, so it would be just visible peeking out of the top of the button-up shirt.
Continuity mistake: When Howard Saint is in the limo after burying his son, he gives instructions to his best friend to kill Jack. His hair is wet and put back with gel. His friend says "all right", then we cut back to Saint, whose hair is now less slick. Cut away and back, and his hair is exactly how it was before.
Answer: The song is "La donna é mobile" from the opera Rigoletto.