Continuity mistake: In the lumber yard, Randy shows a rare streak of genius by knocking out the bad guy with a 2x4 shoved through a stack of boards. When the 2x4 strikes Ringel, it stops its slide protruding about six inches from the stack. When the camera angle changes for the very next shot, the 2x4 is suddenly sticking out more than a foot. (00:39:30)
Plot hole: It's out of character for Monk, a chronic stickler for details, not to correct an error, especially one relating to his own life. Marcy's diorama for "Mr. Monk & the Three Pies" includes Natalie, who wasn't around yet when "Three Pies" occurred. The doll should be of Sharona, but since that would ruin the ensuing joke, Monk is allowed to overlook it. He's aware of Marcy's unreasoning obsessions, but Monk's OCD would simply not permit him to keep quiet about a mistake that glaring.
Continuity mistake: After Monk tries to get out of the contract with Murderuss, he walks to Stottlemeyer with jewel necklaces around his neck. In the next shot (after Stottlemeyer asks "How did that happen?"), the necklaces have disappeared. (The golden teeth stay, though).
Continuity mistake: While Monk and co. question Vicky's roommate, two throw pillows behind her on the couch shift their orientations several times from shot to shot. The larger one also moves from the couch corner to a spot behind the woman's left arm and then back again. (00:14:00)
Factual error: While the police are investigating the murder at the start of the episode, the police make numerous mistakes with the crime scene. First there is no sheet over the body and/or tent to cover the body. Being they are on a beach it would make sense to cover the body from any debris or sand disturbing the body. Second, the sun is shining brightly would not help with preserving the body for the coroner. Finally why have the police only cordoned off a small area around the body. Being a crime scene and potential evidence could be found it makes little sense why they wouldn't cordon off the beach or most of it from the public.
Continuity mistake: In the first shot, when the captain is chatting on the computer and Monk is looking at him through the glass, the webcam we see is white and round. In the next scene, when Monk goes into the captain's office, the webcam is now gray and square.
Continuity mistake: In the mausoleum, the bald man asks Monk and Natalie what happened to the cremation urn name cards, and bends to pick one of them up from the floor. There are no cards on the table when he does this, but in the next shot, four cards have appeared on the table out of nowhere. A short time later, they've all disappeared again. (00:18:45 - 00:20:15)