Mr. Monk Takes Manhattan - S3-E1
Deliberate mistake: After Monk and Sharona speak to Gratnik in Dumbo, they take the subway back to Manhattan. While Monk is sobbing, in the first exterior shot the "A" train slows into the 42 St station in Manhattan; note the "A" at the left with the driver on the right, as well as the "42" station sign not reflected backwards, all revealing a flipped shot. Then it's the "C" train when it stops, with Monk and Sharona back in Brooklyn, even further now at the "Hoyt-Schermerhorn Street" platform (used for TV shows and films), in lower Downtown Brooklyn. (00:21:55)
Mr. Monk and the Panic Room - S3-E2
Deliberate mistake: All the dishes that are usually neatly arranged in Monk's kitchen cupboards (pots, pans, stacks of plates etc.) have been replaced here by cheap plastic ware, so that Darwin the chimp can pull them all out and throw them. Though we hear shattering-glass sound effects as they supposedly hit the floor, the dishes Darwin bangs together and throws are very obviously plastic.
Mr. Monk and the Blackout - S3-E3
Deliberate mistake: As Monk is using the night vision goggles in his house the lights suddenly come back on and continues on still thinking that the intruder cannot see him. The light coming on should have blinded him or at the very least he should have been able to tell there was more light than before even if he hadn't had much experience using the goggles. All the lights in the house come back on and the amount of light would be too noticeable with night vision. This would have been deliberate as Monk continues to think the intruder still doesn't see him in the dark and is part of the joke in the scene.
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.