The misunderstanding between Vincent Gambini and Judge Haller regarding the two "youts" was in fact a real conversation between Joe Pesci and director Jonathan Lynn. Lynn, who is British, at first had a hard time understanding Pesci's pronounced New York accent. He decided that the routine was quite funny and put it in the film.
Despite their characters clashing in this film, Joe Pesci who plays Vinny and Fred Gwynne who plays Judge Chamberlin Haller were actually good friends in real life until Gwynne's passing on July 2, 1993.
When Vinny is trying to explain his "real name" to Judge Haller, he knocks over the judge's chess board. This was accidental but director Jonathan Lynn thought it was so funny and authentic he decided to leave it in the film.
Director Jonathan Lynn actually has a law degree and insisted the film's legal proceedings be realistic. In fact, many attorneys and law professors have praised the film for its accurate depiction of trial strategy and courtroom procedure, especially with regards to presenting expert witnesses at trial. In fact, the film has been screened at some law schools to illustrate courtroom procedures.
The American Bar Association's publication, the ABA Journal, ranked the film #3 on its list of the "25 Greatest Legal Movies.