Continuity mistake: The shots don't match when Monk gets out of bed to go out and confront the UFO enthusiasts. The position of the bed covers changes noticeably between the close-up and the wider shot. (00:36:20)
Continuity mistake: When Mr. Monk enters the Sheriff's office, he is seen straightening out the shades on the front door, so that they are both even about half way down the window. When the Sheriff opens for the woman that was concerned about her relative, in the first shot the right window shade is now pulled all of the way down. Then, when the Sheriff closes the door, both of the shades are now even once again about half way down the window as before.
Continuity mistake: When the gunman is shooting at the Jeep, he hits and deflates the near side rear tyre. His only shot after this wounds the sheriff. Yet when Monk is walking next to the Jeep, both tyres on this side are flat. Then when Monk starts going for help, the two tyres on the other side are now flat.
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.