Mr. Monk Goes Back to School - S2-E1
Other mistake: Derek tells Beth to meet in their "usual spot" the next day at 8am. The next scene has Derek sitting at his desk and it looks like the kids are already in deep with their SAT tests. Beth falls at 8:25am (as per the clock in the testing room.) There is no way that Derek could have killed Beth, put her on the minute hand (later in episode on the Monk recap, it has 8:15am. If Derek was proctoring a SAT test, I don't know of any that start around 8:20 and immediately in depth.
Mr. Monk and the 12th Man - S2-E9
Other mistake: In the scene where Mr.Babcock is murdering the woman in the cinema, we see the woman has a big bucket of popcorn. As he starts strangling her, only a small amount of popcorn falls out. When the camera turns toward the floor there is a lot more popcorn on the floor and it it is spread right across the screen.
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.