Continuity mistake: During the scene that takes place at the party were Connie is singing the song about the instruments, Vincent Mancini and his mother can be seen arriving to find out their names have not been listed to attend. The shot switches back to Connie singing, and Vincent's mother can be seen at a table enjoying the song and festivities. It then cuts back to the entry hall where Vincent begins to shove people around, and his mom is still standing there looking upset that they have not been admitted to the affair.
Continuity mistake: In the sequence of the attack on all the Dons in Atlantic City, three Dons can be seen being shot in the beginning of the shootout, a few moments later, you can see the same three Dons being shot again. (01:00:00)
Continuity mistake: When Mary and Vincent sit in a café and Mary asks him if he is going to keep an eye on her his hair sometimes falls over his forehead, sometimes not. (00:52:20)
Revealing mistake: Several newspaper spins show Michael Corleone in the headline, but a screen shot reveals body copy that is unrelated or outdated. For example, the headline dated 1979 has copy referring to events occurring in the 1990's. Another has body copy with instructions from a software manual.
Factual error: When Keinszig (Swiss banker) gets killed, they knock over a pile of money including US dollars. They show US $100 bills with one problem - Ulysses S. Grant is on them. Benjamin Franklin should appear on the $100 bill. Grant is on the $50 bill. (02:28:45)
Continuity mistake: At Michael's celebration there is a scene of a family photograph taken on the stairs of his home. When the photographer is taking the picture of the family, you can see that the camera he is using is a Sinar P1. But when the scene's angle is reversed, you see the front of the camera, and it is a completely different one - a Toyo-View G.
Other mistake: Before Joey Zasa is murdered, an altar boy in the parade (on the left side of the screen) can't help but stare at the camera all the time.
Continuity mistake: When Altobello asks a young boy in Sicily to imitate a donkey, he is served a jar of wine with the handle pointing to the left side. In the close-up it points to the right side.
Other mistake: In the Mafia World, Vincent would have never been appointed boss of a family without first being initiated as a full member of Cosa Nostra, working his way up the ladder from soldier to Capo, etc. As far as we know, Vincent, from the beginning, was only an associate working for Joey Zasa, then starts tagging alongside Michael, who gives him control of the Corleone Family later, after his failing health.
Other mistake: In the mafia world of Cosa Nostra, anyone that puts their hands on a made member, especially a low-level associate such as Vincent, would be immediately killed. Vincent would not have been allowed to live for viciously assaulting a mafia Capo, as was the rank of Joey Zasa in the film. Not even Michael could have saved him from such a fate had this been true.
Answer: It shows you how greedy they are even as they've made it to the zenith of their criminal careers. That's why you see Michael pass it on disgustedly and stare blankly into the ether. Michael's goal was never to be the boss or capo di tutti capi, he only did it to protect his father and then his family, his main goal. And at that moment he realises he's never getting out. He's a business man in a world of criminals (which he is himself).