Factual error: When Monk visits the prison for the first time, he is searched, passed, and has a mini-panic attack because people have touched him. Sharona steps forward to comfort him, and she puts her arms around him. This is a very serious breach of procedure and it is not possible for the guards to miss it, because Sharona has not been searched. It's a common technique for trying to pass contraband called 'a touch through' - a person with an item to be smuggled into the prison (drugs, usually), passes them on to a person who has been searched and is therefore 'clean'. Monk would be taken back to the guard's station to be searched again. He would not be allowed leniency because the guards happen to know or to like him - visitor ingress and egress is always done under CCTV and the guard would know he was being watched - quite possibly by someone who doesn't know who Monk and Sharona are.
Plot hole: Death row prisoners cannot donate organs. No doctor participates in an execution and after the lethal injection the medical examiner must wait at least fifteen minutes to test for cardiac activity before pronouncing the prisoner dead. This is enough time for hypoxia to render the heart, lungs and kidneys useless for transplant. Apart from this, organs intended for transplant must be removed within minutes of the death of the donor. Prisoners are not executed in operating theatres.
Continuity mistake: When his wife visits Stottlemeyer in his office he fills the running waterfall with coffee, but later in that scene when he holds her hand to promise her that he will investigate the the old man's death the waterfall is empty again. (00:04:40 - 00:07:10)
Factual error: There are a number of unrealistic situations portrayed inside the prison: 1) An inmate scheduled to be executed in less than an hour would not be left so unattended as to require the trustee to yell for help when he went into distress, or to allow the inmate and trustee to exchange objects. 2) A chronic rule-breaker like Spyder, who had just "put a guy's head through a wall," would not have gotten just one day in solitary confinement with no other loss of privileges. 3) The neo-Nazis would not be allowed to wear swastika lapel pins. 4) Death row inmates are not served their last meal by unescorted fellow prisoners.
Deliberate mistake: All the mail bombs are delivered in packages tied with knotted string. The USPO hasn't allowed string-tied packages since the mid-90s (they get caught in automated equipment), but since the knots were crucial to ID-ing the suspect in this episode, that fact had to be ignored.
Continuity mistake: In the cemetery scene, Stottlemeyer approaches the grave of the 17 year old open case hit and run victim. The dates on his grave are 1980-1997. But in Dennis Gammill's confession letter in the end, it says he killed the boy in December 1998.
Continuity mistake: In this episode Randy is allergic to cats, in fact he has an allergic reaction even if a cat has been there lately but is not there now. But in Mr. Monk and the Sleeping Suspect, during the scene where Monk and the police are investigating the woman's destroyed house, a cat passes within a few feet of Randy, who doesn't sneeze or show any signs of his allergy.
Factual error: When Stottlemeyer backs up the video tape at Monk's house, we can hear the sound chattering backwards. Only a huge industrial (studio) machine would do that. Little home VCRs, like Monk's, mute the sound during in-play rewind and fast forward modes. (00:34:30)
Continuity mistake: When Monk is leaving Derek Philby's classroom, he is quite content to just pick up a piece of chalk (with his bare hands) to write on the blackboard, but earlier, he makes sure to use a chalk holder to do this and nearly has a panic attack when he gets chalk dust on himself.
Continuity mistake: A fight breaks out in the prison laundry, and Monk crawls into a giant dryer to hide, pulling the door mostly shut after him. But in the very next shot of the fight raging on, the dryer door is visible in the background - wide open. Next shot after that, it's shut again, and Monk sneaks it open to peek out. (00:42:00)
Continuity mistake: When Monk spills the potted plant and grabs a vacuum cleaner from the hall, he's holding the handle with several large paper towels. When he plugs the vacuum in, he now has a wipe in his hand instead. When he's finished plugging in and turns around, the wipe has vanished and there's nothing in his hands or on the vacuum. But when we cut to a wider shot as he turns the vacuum on, the paper towels reappear on the handle.
Deliberate mistake: Joshua Skinner hid a fortune in gold by melting it down, mixing it with ink and writing it into 947 journals. Monk's producer concedes that in real life, 947 journals would probably hold "only about $11 worth" of gold-laced ink. But the idea was so amusing that he couldn't resist using it anyway. (00:42:00)
Factual error: In this episode, when Sharona and Monk arrive to visit his brother, they talk about the swing set. Monk tells Sharona that his father put up the swing when he was 8 years old but this is a much newer swing set. Look at the curved plastic seats: these have come about in the last six to eight years. It also doesn't look at all rusty like a 40 year old swing would.