Mr. Monk and the Airplane - S1-E13
Continuity mistake: "Nationwide Airways" is the name of the fictional carrier used in the episode, and it even has its own logo and livery. Yet in the exterior shot of the plane pushing back from the gate, it has suddenly transformed itself into a Delta Air Lines plane. It also looks like a 1990s Delta plane while it is taking off. (00:13:05 - 00:15:00)
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 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 Candidate (2) - S1-E2
Other mistake: When Monk is climbing the ladder to pursue the killer, at a couple of points, he wipes a rung, then grabs the one above it. (00:18:15)
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
Continuity mistake: When Monk is in the review board hearing, in long shots, the wastebasket by the board members' table is empty. When one of the reviewers throws away a paper that misses the basket and lands right next to it, there are several papers already in it. In the next long shot and for the rest of the scene, the basket is empty again and the missed paper is at least two feet away. (00:06:15 - 00:07:40)
Mr. Monk Goes to the Carnival - S1-E5
Continuity mistake: When Kitty runs up to Gitomer, she is not wearing gloves. Later, when Monk gives his summation, careful viewing will show Kitty wearing a glove that's used to hold the knife.
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?
Mr. Monk Goes to the Carnival - S1-E5
Other mistake: Kitty, the killer, is seen running to Gitomer after Lt. Kirk leaves him. She is supposedly running to stab him, but you can see that both of her hands are empty as she dashes to his side.
Mr. Monk Goes to the Asylum - S1-E6
Visible crew/equipment: When Monk is on the roof and helping the guy not to fall, you can see that he is tied off with a rope.
Mr. Monk and the Other Woman - S1-E8
Audio problem: When Monk finally turns around at the funeral to tell the old man behind him to be quiet, you can still hear the man coughing. But the man's face is still, and his mouth is not open, and he isn't making the sound.
Mr. Monk Takes a Vacation - S1-E10
Continuity mistake: When Monk is talking to Benjy, he buttons up the top two buttons on his shirt, but in the next shot of him they're undone, and he's re-buttoning them.
Mr. Monk and the Billionaire Mugger - S1-E7
Continuity mistake: When Stottlemeyer pulls his gun on Mr. Modine, the safety is off and the gun is cocked, but in the next shot it's not cocked and the safety is on. Then we see the safety off, but not cocked.
Mr. Monk and the Candidate (1) - S1-E1
Continuity mistake: When Mrs. St. Claire refers Mr. Monk as "Rain man", her glass is about an inch and a half full. Next time we see her the level of liquid has dropped. (00:16:45)
Mr. Monk and the Airplane - S1-E13
Factual error: Though anti-freeze is lethal it does not kill quietly and fast but rather agonizingly, painfully and slowly, inducing vomiting and fever. (00:30:30)