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: The two men are trying to work out a secret deal between them without involving the union, which means the workers' interests aren't being represented and defeats the whole purpose of a union. The mayor would lose labor's support and Cusack's union troubles would just be starting.
Captain Defenestrator