Character mistake: Stottlemeyer says that the human finger was "still bleeding, freshly severed." But prior to him saying this, when we are shown the finger, there is no bleeding whatsoever and the blood on the severed end had already dried.
Mr. Monk vs. the Cobra - S3-E11
Character mistake: Monk says that Croatia is a new country and didn't exist until 1992, but Croatia gained independence in 1991. However, Croatia still existed prior to that, it was just part of the Socialist Federal Republic of Yugoslavia. So things could still be made in Croatia.
Mr. Monk and the Election - S3-E15
Character mistake: Captain Stottlemeyer uses gloves to pick up the letter found sticking out of the pipe. He doesn't actually put the glove on, but still uses it to avoid getting any of his prints, skin, etc on the paper. But then he uses his other, non-gloved hand to open up the note and hold it, and Monk also touches the letter. If he cared about not contaminating evidence by using the glove, he wouldn't touch it bare handed and if he didn't care about touching the note bare handed, then he wouldn't have used the gloves.
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.