Mr. Monk Goes Back to School - S2-E1
Deliberate mistake: When Monk is first teaching his class, the class goes for less than 10 minutes.
Mr. Monk and the Sleeping Suspect - S2-E7
Deliberate mistake: All the mail bombs are delivered in packages tied with knotted string. The USPO hasn't allowed string-tied packages since the mid-90s (they get caught in automated equipment), but since the knots were crucial to ID-ing the suspect in this episode, that fact had to be ignored.
Mr. Monk and the Paperboy - S2-E10
Deliberate mistake: When Sharona spots Disher's personal ad in the newspaper, there is a shot of it. She then reads the description of him from the ad, which matches what's on the screen, however, the second part she reads, "Seeks petite blond with no-nonsense attitude, kids ok" is not in the ad shown. (00:22:20)
Mr. Monk Gets Married - S2-E15
Deliberate mistake: Joshua Skinner hid a fortune in gold by melting it down, mixing it with ink and writing it into 947 journals. Monk's producer concedes that in real life, 947 journals would probably hold "only about $11 worth" of gold-laced ink. But the idea was so amusing that he couldn't resist using it anyway. (00:42:00)
Answer: Notice also that in the opening credits scene when he is touching parking meters her also wipes his hand on his clothes each time he does it.