Plot hole: It makes no sense why the police haven't done the most obvious thing and checked for fingerprints on the murder weapon (the knife). It would not only back up the detective's claim that he did not stab the victim (he never touched the knife) but would have given the police a major clue to finding and prosecuting the murderer.
Continuity mistake: When Monk is in the review board hearing, in long shots, the wastebasket by the board members' table is empty. When one of the reviewers throws away a paper that misses the basket and lands right next to it, there are several papers already in it. In the next long shot and for the rest of the scene, the basket is empty again and the missed paper is at least two feet away. (00:06:15 - 00:07:40)