Mr. Monk and Little Monk - S4-E8
Factual error: In the flashback where Monk is explaining how the money was stolen, the principal finds the 5 dollar bill he wrote "good luck" on and holds it up for everyone to see. The bill he holds is a 5 dollar bill which was released in 2000, with the enlarged Lincoln. The flashback takes place in 1972.
Mr. Monk and Little Monk - S4-E8
Factual error: When Monk is talking to Sherry about the painting in the art gallery where the painted woman was going to kill her husband, he says that she has a bruise on her left eye. But the bruise is actually on her right eye. While it is viewable that it is on Monk's left, he would not make that mistake.
Mr. Monk and the Astronaut - S4-E14
Factual error: During their examination of the crime scene, neither Monk, Stottlemyer, Sherona, Randy or anyone else in the room wear gloves or any kind of other protective clothing. They handle artefacts that could be critical to an investigation of the woman's death, including a cheque made out to her, and they hopelessly contaminate them by doing so.
Mr. Monk Gets Jury Duty - S4-E16
Factual error: Since Monk has OCD it would be highly unlikely for him to be on a jury. Plus, Monk works for the police department and since he technically works in the criminal justice system, that would have made him exempt from jury duty.
Suggested correction: First, he would have to ask for exemption in writing prior to serving, with proof, regarding hardship for his OCD. While it's possible his doctor might say serving jury duty would result in physical harm due to his mental illness, it's unlikely to be given by Dr. Kroger. And Monk is not an active peace officer, so that wouldn't earn him an exception.
Mr. Monk Gets Jury Duty - S4-E16
Factual error: When Natalie hears the jury's muffled screams inside the locked room she uses the fire extinguisher to tear off the door knob. But a locked door without a knob is actually only harder to open, because like that you cannot turn the mechanism even if it was unlocked.