Audio problem: At the start, the car stops at the gas station (weirdly far from the pumps, for a start). Grooms talks to Monk then walks to the back holding the nozzle, stretching the hose taut, despite no filler cap on that side of the car. We cut to Monk, and we hear a clunk of Grooms attaching the nozzle (to what?). Later Grooms is still holding the nozzle, and as Monk goes inside Grooms is just wandering around aimlessly holding it.
Factual error: Randy calls the cabin and gets a "not in service" message. But he should have heard an unanswered ring instead. The FBI agent tore the cord from the wall, which in the US does not generate a "not in service" recording. That only occurs when the phone company cuts off your service due to non-payment or cancellation. (00:30:00)
Continuity mistake: After Stottlemeyer says "Well I'm gonna make the most of it" (when he is talking to Monk in the backyard of the cabin and Monk is cleaning) he looks a little to his left and opens a beer can while his mouth is shut. In the next shot he is looking in a different direction and is smiling a toothy grin.
Other mistake: When Stottlemeyer is about to eat his cake he is looking at Monk. Shortly before he starts to pick up a piece of cake you can see he is pretending to chew a piece in his mouth. Throughout the scene you can see Stottlemeyer's face and the cake. At no point before he pretends to chew does he put a piece in his mouth.
Continuity mistake: When Randy and his 'girlfriend' are having take-away (take-out) food, the girlfriend says, "Before he died, he said he's always look out for me". As she says this, her arms are resting on the table, but in the next shot her elbows are on the table and her hands are together just under her chin.