Prosecuting attorney Trotter is played by the late Lane Smith, whom most TV Tropers probably associate either with the Richard Pearce film The Final Days where he played Richard Nixon, or (more likely) with Lois and Clark where he played Perry White. Great shades of Elvis! Younger tropers may remember him better as Coach Reilly in the first The Mighty Ducks movie.
The director, an Englishman, was casually chatting with Joe Pesci and got confused by his Brooklyn-accented pronunciation of "youth". After Pesci explained it, they both realized they were having a conversation that should be in the film. The famous "two yoots" conversation between Vinny and Judge Haller which resulted is practically verbatim what Pesci and the director said to each other.
According to the director's commentary, the screech owl that woke Vinny just happened to come across the film crew one night. It stayed because they fed it some meat.