Mr. Monk and the Three Pies - S2-E11
Corrected entry: The scene where Monk and van Ranken attempt to recreate the scene of the murder to find a bullet is impossible. Side-ejecting ammo can land anywhere and therefore they could never have found the bullet.
Mr. Monk Goes Back to School - S2-E1
Corrected entry: 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.)
Correction: Not all the letters in the word reminder were capitalized. It was written "ReMiNDER."
Mr. Monk Goes to the Theater - S2-E6
Corrected entry: When Sharona is talking to her mother at the table and her mother spells out S-T-O-L-E, Sharona says he (Benji) can spell, he's 11. This episode aired in 8/2003. In the pilot episode, which is from 7/2002, she says he's 11 in that episode, too, which is impossible because it's 13 months later.
Correction: This can not be a mistake unless they actually say what year it is in the show, or confirm that a more than a year has passed within the show. Just because 13 months has passed in real life it does not mean that much time has passed in the show.
Mr. Monk Goes to the Circus - S2-E4
Corrected entry: Throughout the entire show, Monk says he is afraid of milk (he says it in "Mr. Monk and the Candidate"). However in "Mr. Monk Goes to the Circus" he asks for milk and cream in his hot chocolate. But in later episodes his fear of milk is still there, so it's not that he's managed to make progress in that area.
Correction: Monk's fear of milk is not based on the taste of milk, but on its texture, and the way it slops everywhere when you pour it. Hot chocolate with milk in it has quite a different texture, and it wouldn't spill everywhere as Monk has no need to pour it.
Correction: It's an irrational fear, it doesn't have to be consistent.
Correction: Sharona actually says at one point "We've made a lot of progress with milk."
Correction: His fear of milk is because it's like human breast milk, therefore full of bacteria. Also from a naked breast, even if from a cow. The act of milk being heated up for hot chocolate is the same as cooking out the bacteria of raw meat. It doesn't have to make sense that all milk is pasteurized. He actually tastes that it is hot, so now clean.
Correction: And those chocolate drinks are made with water and a powder containing milk powder but not milk.
Mr. Monk Goes to Mexico - S2-E2
Corrected entry: Monk and Sharona drive to San Marcos, a Spring Break resort town in Mexico. At the border, they're pulled over by Mexican authorities for a Customs inspection. Such inspections are performed on the US side of the border, but during the search, it's made clear that not only are they already in Mexico - they're also, conveniently, already in San Marcos. Spring Break resorts like this one, with pools, hotels, etc., aren't located at the border. (00:10:00)
Correction: Although they may not always take advantage of it, Mexican authorities absolutely have the right to perform customs inspections at their own border. And San Marcos is a fictional resort. There is no rule about where it must be located.
Correction: I think that's the point - side-ejecting ammo can land anywhere which is why, when van Ranken couldn't find the last shell, he assumed (incorrectly) that it must have landed in one of the pies. The scene of him throwing the shells up in the air was simply to help spur ideas of places it might have landed that he might not have thought of - including the flour.