It is an awkward scene, Puppeteer. But it occurs to me that it might be understood in the context of a major subtheme of GFIII: how Vincent and Michael used each other.
Vincent, egged on by Connie, forced himself on Michael so that he could move up in the world. He crashed the party, probably because he (or more likely, Connie) knew Zasa would be there bad-mouthing him. Instead of accepting reconciliation with Zasa, he bit his ear. This forced Michael to choose between protecting Vincent or leaving him to Zasa--Michael probably would have preferred to have nothing to do with either Vincent or Zasa. Michael seemed amused to have Vincent around as a general gofer and protege. But after the Atlantic City shootup and Michael's seizure, Vincent saw another opportunity to ratchet up his career--by enlisting Neri's and Connie's support to kill Zasa while Michael was unable to stop him. That act forced another inimical choice on Michael: dump Vincent or promote him. Meanwhile, by romancing Mary, Vincent was trying to force Michael to accept him as a real family member instead of an illegimate hanger-on. But by that time, Michael realized that his "true enemy" wasn't a common pazzo like Zasa, but a dangerous combination of Altobello, Lucchesi and various nefarious figures associated with Immobiliari and the Vatican Bank. He also realized that his own failing health was a big handicap. His life was in danger. He also was terribly frustrated: "Just when I thought I was out, they pull me back in." Michael really wanted out. How to stay out? He anointed Vincent as his successor. That way, Vincent would take the responsibility of protecting Michael, take the risks and be the target. Oh, and there was a quid pro quo: Vincent had to dump Mary. If things had worked out the way Michael wanted, the Vatican would have approved the Immobiliari deal, Michael would have been completely legit (and filthy rich), and Vincent, after killing Michael's enemies, would have become the heir to the semi-legit and non-legit remnants of the Corleone empire, the lightning rod for Michael's criminal former associates and potential enemies--and history as far as Mary was concerned.