Mr. Monk and the Psychic - S1-E3
Plot hole: When Monk is looking for the pebble, he immediately makes an announcement through the shop's speaker system and then directly asks the guy wiping the floor where the rest of the garbage is. Given the size of the trash can it is not realistic that the guy wiping could have filled the trashcan, emptied it and have it filled half again in the 2 to 10 minutes that might have passed since the pebble got lost.
Mr. Monk Goes to the Carnival - S1-E5
Plot hole: It makes no sense why the police haven't done the most obvious thing and checked for fingerprints on the murder weapon (the knife). It would not only back up the detective's claim that he did not stab the victim (he never touched the knife) but would have given the police a major clue to finding and prosecuting the murderer.
Mr. Monk Goes to the Asylum - S1-E6
Plot hole: Monk and Manny go on the roof through Manny's window to grab a piece of cloth. Due to the possibility of suicide, it is highly unlikely that an asylum would have a window that goes directly to the roof, unlocked.
Mr. Monk and the Other Woman - S1-E8
Plot hole: Monk says that the two files, both with tab at the middle, were kept together, which led him to discover that the person related to this file is 'the guy'. In an earlier scene, when Monk is searching the file cabinets, he picks up one of these two files and tells Sharona that this file is of 'the guy'. How can he say which one of the two files with middle tabs, which are put together, is related to 'the guy'? Impossible. (00:39:00 - 00:40:00)
Mr. Monk and the Other Woman - S1-E8
Plot hole: Monk's led to the killer because he figures out that he "added a file" to the lawyer's filing cabinet, judging by the left/middle/right tabs being off. But this makes no sense on two levels - firstly why would he need to add a file? He was just replacing the real will with a forgery. He just took the old one out and added the new one, he didn't need to mess with the filing system at all. Secondly, he picks that one out because the tabs are offset, but what if the lawyer had just taken on a new client or added other paperwork? Then the tabs would be off too, but that never seems to be considered.
Mr. Monk and the Red-Headed Stranger - S1-E12
Plot hole: When Monk explains to Miss. Mass how she had murdered Sonny, a flashback of the crime shows that she isn't wearing gloves when she leaves the note to get him to go to the alley. Had the cops checked the note for prints, they would have shown Miss. Mass' fingerprints on it and knew she was responsible for Sonny's death.
Suggested correction: Just because they lifted fingerprints off the note, there wouldn't be a way to identify them as belonging to Ms. Maas if her prints aren't in the system. As a witness (and ruled out as a suspect because they thought she was blind), they wouldn't have fingerprinted her just because the found unknown prints and wanted to rule her out.
What about gun residue on the hands?
