The misunderstanding between Vincent Gambini and Judge Haller regarding the two "youts" was a real conversation between Joe Pesci and director Jonathan Lynn. Lynn, who is English, 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.
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. Additionally, the film has been screened at some law schools to illustrate courtroom procedures.
Gambini's cross examination of Sam Tipton (grits), Ernie Crane (dirty windows), and Constance Riley (glasses) represents technically competent impeachment of the prosecutor's witnesses. Overall the film does an excellent job, though abridged and succinct, of representing the criminal judicial process.
According to director Jonathan Lynn, the eastern screech owl in the scene in the woods was a real owl that had a little prior training so it wouldn't be scared away by the gunfire. The crew got it to open its mouth by giving it little pieces of beef, and artificially induced screeches were added to the film in post production. The owl's reaction to Vinny shooting the gun was authentic and needed only one take. The director states on the DVD commentary, "we got amazingly lucky with that screech owl".