Randy is easily visible removing his coat in the room behind Monk and Stottlemeyer only seconds before the shot switches to him walking into the same room and taking off his coat again.
When Vicki leaves Kevin drugged asleep in the car on the train tracks, the wide view shows the car is on the tracks furthest from the camera. When Monk switches the tracks to keep the train from hitting the car the train is switched to the tracks furthest from the camera.
(#2.10), Vicki says that she and Kevin got blood tests in order to get married, but California does not require blood tests for a marriage license.
When the car is parked on the railroad tracks, they race to move the switch and detour the train. Track switches are padlocked. It would very rare to find one that was open. Also, the train engineer would make an effort to stop the train seeing the car on the tracks.
Train track switches are located right next to where the tracks split, rather than several yards away as shown.
Kevin Dorfman is making "mushroom moussaka" and is rattling off the ingredients. He never mentions mushrooms but strangely mentions eggplant.
When Monk is giving the summation of the murder of the paper boy, it shows Kevin opening the door to Vicki and she is obviously street level. But when Kevin is introduced earlier, it is announced that he is Monk's upstairs neighbor. He couldn't be an upstairs neighbor if looking out the door its street level.
When Sharona is reading Randy's personal ad, a close-up of the ad shows that she reads the entire thing, but a few seconds later she leans over and reads an additional line that was not in the printed ad.
The rolling stock on the train is of a design not in general use in California since the early 1980s.
It is stated that Jose and Nestor have been delivering Monk's newspaper for two years, but Nestor somehow doesn't know the protocol for delivering Monk's paper by now.
Reflected on the side of the damaged car in the garage as Monk and his team enter to make an arrest.