Mr. Monk and His Biggest Fan - S6-E1
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.
Mr. Monk and the Naked Man - S6-E3
Plot hole: SPOILER Arlene Boras swaps Peter Magneri's MRI scans for those of a healthy person in order to hide the fact that he has a potentially lethal aortic aneurysm. Clearly visible on the MRI scans she is holding are the dates and times of the examination - and the name of the patient. Swapping the records is pointless.
Mr. Monk and the Wrong Man - S6-E8
Plot hole: Monk supposedly hears for the first time that Max was not carrying anything away from the crime scene when he speaks to the witness in front of the church. This leads him to conclude that there must have been a 2nd man with Max 14 years ago. But this does not make sense given that the witness with her photographic memory did not change her testimony and given Monks ability to observe and memorize details it is very unlikely that he did not come to that conclusion 14 years ago already. (00:32:45)
Mr. Monk and the Man Who Shot Santa - S6-E10
Plot hole: This episode's entire story line takes place in the six days before Christmas (Dec. 19-24). "Bad Santa" is shot in the right shoulder on the 19th, sustaining a wound serious enough to require wearing a sling for the next several days. Yet at the end, a mere few days later, he's recovered enough to have a knock-down-drag-out fistfight with Monk, wielding a knife and throwing powerhouse punches with his wounded arm as though no injury had ever occurred. (00:38:00)
Mr. Monk and the Three Julies - S6-E13
Plot hole: There is no other reason for Randy to hand Natalie the walkie-talkie but to fill that plot hole. He is in fact in breach of police rules when he hands his department issued radio to a civilian to answer it while he is on duty. The same goes for Stottlemeyer and the car keys he hands to Monk. Even more so since he knows Monk could not even drive that car to the side in the far fetched scenario that a police car had to be moved while the cop is serving a warrant inside the building the car is parked in front of. (00:01:15)
Mr. Monk Is on the Run (1) - S6-E15
Plot hole: *Spoilers* Monk and Stottlemeyer cook up an ingenious plan to make Monk appear dead, but how the fugitive Monk acquires his regular clothes (in place of Mitch's uniform), the bullet-proof vest and the gun is not addressed. The police are watching Monk's apartment, Disher is watching Natalie and Julie, and Sheriff Rollins is watching Stottlemeyer, leaving us to wonder just how they managed all this right under their fellow cops' noses. (00:43:00)
Suggested correction: Stottlemeyer is a police captain. The sheriff can't watch his every move, and there are still plenty of cops who are loyal enough to Stottlemeyer for him to get one of them to deliver them to Monk or leave the items somewhere for him to retrieve.
Nice theory, but there's absolutely no hint of it in the episode. The lack of any explanation creates a bit of a plot hole because it leaves us wondering.
Mr. Monk Is on the Run (1) - S6-E15
Plot hole: The D.A. says that ballistics show that the bullet came from Monk's gun. The simplest thing to do would be to look at the gun, they'd know that it hadn't been fired and was full. With Monk's OCD we know it was cleaned, and the sheriff came in right after, so Monk couldn't have reloaded it. Yet they overlook all of this.
Mr. Monk Is on the Run (2) - S6-E16
Plot hole: When Stottlemeyer is confronted by the Sheriff for not going to the morgue there are 2 plot holes in that one scene: first it is impossible for that article to be in the morning paper since the coast guard "just fished him out" last night. And secondly an article, especially a long article like the one about the body in the bay would contain a physical description of said body. That is the reason it does not make sense to even ask the captain why he did not go to check the body to see if it was Monk when the body was tattooed and had red hair. (00:13:30)
Suggested correction: The article being there that fast is a bit odd, the sheriff mentions a police alert had been put out and was why he went to the morgue. That was what he was confronting the captain about. Even without the article the point of why he didn't check is still a valid question.
Do you really believe that the police alert did not include a description of said corpse being found for the missing person's unit to combine against their lists?