Mr. Monk and the Big Game - S5-E3
Character mistake: When Julie asks "who discovered DNA?", Captain Stottlemeyer says "Watson and Crick. Two British scientists." However, James Watson is American (as of 2021 he's still alive), not British. And the duo only discovered the structure of DNA, not DNA itself. As much knowledge as the Captain demonstrates on the subject, he should know these two facts at least.
Mr. Monk Meets His Dad - S5-E9
Character mistake: At some point Monk asks his father what the device in the car is. His dad tells him it's a GPS. It's difficult to believe that our detective doesn't recognize the machine, even if it's probably another model: the whole plot of the episode 2x03, Mr. Monk Goes to the Ballgame, revolves around a tampered-with GPS.
Mr. Monk Makes A Friend - S5-E11
Character mistake: At the crime scene, the #8 evidence marker is in the bathroom. When Monk and the Captain are examining the body, a #8 evidence marker is seen on the lamp. They wouldn't use a number more than once at a crime scene.
Mr. Monk Visits a Farm - S5-E14
Character mistake: When Randy Disher is having Chinese food in his apartment with his new girlfriend in 3-12 "Mr. Monk Gets Cabin Fever", he gets a fortune stating that he is going to get money from his uncle, and says that he doesn't have an uncle. In this episode Randy inherits a farm from his uncle who appears to have committed suicide, but was actually murdered.
Suggested correction: Randy says when that uncle dies that they were never close, so his leaving him the farm comes as a total surprise. It's still a character mistake, however, Randy is established as the sort of person who could "blank out" a relative that long-lost.
Randy says he can run the farm because he went there and helped his uncle every summer.
Mr. Monk Goes to the Hospital - S5-E16
Character mistake: The doctor remarks that his patient has rheumatoid arthritis early in the episode, and later he says osteoarthritis. These are two different conditions. (00:19:15 - 00:28:40)