Other mistake: In Tiffany's converted garage, Tiffany says she's thinking of putting in a ballet bar, but there's one there already right next to the big mirror, where it's supposed to be.
Other mistake: When DeNiro is discussing a bet on a future (7 weeks away) game between the Eagles and Cowboys, DeNiro points out that the Eagles are favored by 1.5 points. In fact, betting lines are not set on games until the previous week's games are played, because there may be a major injury which would affect the line. As a bookmaker, DeNiro would certainly know this. And bookmakers are rarely fans of teams, and it would be unusual for a bookie to be such a rabid fan as DeNiro is in the movie.
Answer: It's not exactly common, but yes, it would be up to the judge, and establishing that a person is a "clear and present danger to themselves or others" can result in involuntary commitment in Pennsylvania, where the film takes place. In this case, it would not be hard to argue that, "the person has inflicted or attempted to inflict serious bodily harm on another and that there is a reasonable probability that such conduct will be repeated" (50 PA. CONS. STAT. ANN. ยง 7301 (b) (1)), as he had just physically assaulted his wife's lover and she'd obtained a restraining order. His mental health problems would have been well-documented, so it would have been easy for a judge to order him to undergo psychiatric evaluation, which could (and, in the film, does) lead to extended involuntary commitment at the discretion of a mental health professional.