Bitty Schram, Ted Levine, and Jason Gray-Stanford attempted to renegotiate their contracts halfway into the third season. The three actors sat out the episode "Mr. Monk and the Game Show" when an agreement was not reached. Schram was fired after the next episode, "Mr. Monk Takes His Medicine", and replaced with Traylor Howard.
Tony Shalhoub (Adrian Monk) is the only actor to appear in all 125 episodes of the series. In second place is Jason Gray-Stanford (Lt. Randy Disher}, who appeared in every episode except for "Mr. Monk Goes to the Asylum", "Mr. Monk and the Game Show", "Mr. Monk Gets Stuck in Traffic" and "Mr. Monk and the UFO".
The characters and basic structure of the series were inspired by the Sherlock Holmes mysteries. The character name "Adrian Monk" was intended to be unusual like that of Sherlock Holmes. Other characters correspond to Holmes characters: Sharona Fleming (a nurse) and Dr. Watson; Capt. Stottlemeyer and Inspector Lestrade; and Monk's brother Ambrose and Mycroft Holmes (Sherlock's brother).
The characters of Captain Leland Stottlemeyer and Lieutenant Randall Disher (named Randall Deacon in the pilot) serve much the same function in Monk as did Inspector Lestrade in the Sherlock Holmes stories. This relationship may have inspired these characters' names: taking the first two letters of each name in order - LE from "Leland", ST from "Stottlemeyer", RA from "Randall" and DE from "Deacon" - spells out "Lestrade". (However, after the show's pilot episode, Randy Deacon's last name was changed to Disher.)
The show was originally to be made for ABC (the American one) with Michael Richards starring. When he pulled out, so did ABC. However, when the show was successful on the USA network, ABC agreed to carry second-run episodes (much in the same way that USA carries second-run episodes of Law & Order: Special Victims Unit (1999)). This only lasted for a year.
The show's writers occasionally satirize Monk's near-perfect memory. For example, in "Mr. Monk Goes Back to School" he can't remember if a crime scene on a roof is his 4th or 5th worst nightmare, since he "didn't bring the list".
The police station where Stottlemeyer and Disher work as well as a number of crimes throughout the series are said to be located on Vinton Street in San Francisco. However, the real Vinton is in Madison, New Jersey, where series creator Andy Breckman lives.