Plot hole: Monk's dad, Jack, drives an 18 wheeler. In the scene where Jack pulls over to the side of the mountain road so they can discuss specifics about the GPS, a brake line is shown breaking and spurting what I assume is meant to be brake fluid. The rig then rolls down the mountain. However, 18 wheelers don't have brake fluid since they don't have hydraulic brakes, they have air brakes. Even if the rig lost its brakes due to loss of air pressure, the brakes are spring loaded to lock up all the wheels in this case and prevent movement. That's how you set the parking brakes, by releasing the air pressure. In other words, if he has air, he can use his application brakes; if he's lost air, he has his parking brakes set. Rigs that lose their brakes going down steep grades do so due to extreme overheating, causing brake fade, an inability of the brake shoes to grab the brake drums. This wouldn't have happened while they were parked.
Deliberate mistake: In the opening scene, Wood's tie is grabbed by an exposed fan belt located above the side of the engine. However, this belt/pulley assembly doesn't exist in a real truck's engine compartment - the fan belts are all in front of the engine, where the camera can't see them easily. The prop master must have added this dangerous device to the truck to allow the camera to see the strangulation.
Continuity mistake: When Julie talks to Monk on the phone, her hair is down over her right shoulder but swept back behind her left one. When she hangs up and hands the phone to her mom, the hair is suddenly covering her left shoulder instead, and now her right shoulder is bare. (00:17:15)
Other mistake: When Jack Monk is filling up his truck, the numbers on the pump don't add up right and keep changing. The cost is $3.599/gallon, but in one shot you see the sale price reads $93.78 for 28.348 gallons. The sale price should be $102.02. But in a later shot, he's only pumped 27.126 gallons. Then when he hits $100 sale price, it's for 31.259 gallons ($3.199/gallon) but in the next shot it reads 27.719 gallons.
Character mistake: At some point Monk asks his father what the device in the car is. His dad tells him it's a GPS. It's difficult to believe that our detective doesn't recognize the machine, even if it's probably another model: the whole plot of the episode 2x03, Mr. Monk Goes to the Ballgame, revolves around a tampered-with GPS.