Continuity: When Monk is leaving Derek Philby's classroom, he is quite content to just pick up a piece of chalk (with his bare hands) to write on the blackboard, but earlier, he makes sure to use a chalk holder to do this and nearly has a panic attack when he gets chalk dust on himself.

Deliberate "mistake": When Monk is first teaching his class, the class goes for less than 10 minutes.

Continuity: At the school tower murder scene, Randy's coat is buttoned up over his tie, but changes suddenly when Stottlemeyer says, "OK, bring him up." The coat is immediately unbuttoned and open all the way in the very next shot.

Other: When Monk is leaving Derek Philby's classroom, he dots the "I" in "REMINDER" on the blackboard. However, the word was in capital letters, so the "I" needn't have been dotted. Monk wouldn't make this mistake. (And the word is written in plain block sans-serif letters, so he's not adding a missing line: he's definitely dotting the capital I.)