Factual error: As an out-of-state attorney, Vinny would have had to file documents for admission to the state bar association "pro hac vice" ("for this case"), and the boys would have been assigned a local attorney to ensure compliance with the rules of procedure, which Vinny kept violating.
Factual error: In District Attorney Trotter's opening statement he asks the jury to convict William Gambini of murder in the first degree and Stan Rothenstein of accessory to murder in the first degree. There is no such crime in the Alabama criminal statutes. It has to be either Capital Murder or just Murder. Alabama does not have different "degrees" of murder. Also the arraignment and trial are both conducted by the same judge. In the Alabama court system a District judge would have conducted the arraignment, while a different Circuit judge would have conducted the jury trial. It's ironic since the director brags about his attention to detail in the DVD director's commentary. He obviously didn't check it too closely.
Chosen answer: He never says that it was "his" idea. The actual quote from the movie is that on "a" hunch he looked it up. From the way it is worded in the movie, it appears he said it this way in order to appear impartial in bringing any new evidence to the court's attention, not necessarily just information that would benefit the defendant's case.
Jazetopher