In the second scene of the movie where Jesse Stone is driving down the highway, you see him drinking from a coffee cup. He is supposed to be in the USA, but the colors and design on the cup are clearly Tim Hortons, which at the time this movie was made, only had stores in Canada. The design has since changed on the cups, but the design and color scheme at the time are exactly as they appear on his cup.
When Lou parks by the cliff, the distance from his car to the fence changes, and before he gets out of the car the bottle he drinks from has no label. When he gets in the car again it has a label.
When Lou is at the cliff, the fence has three cross rails. When Jesse goes to the scene later, it is a fence with two rails, different locations altogether.
The first time Jesse drives up in front of the Genest home in the police cruiser, he parks behind his Scout, which is visible parked behind the other car.
The first night in his new house, Jesse picks up a full bowl of dog food, then sets an empty bowl down on the counter. He then opens a can of dog food an empties into the bowl. It's possible he emptied the bowl off-camera, but that would have been an easy shot to include, and especially important to drive home the point that the dog was not eating (a point he raises a few scenes later).
Joe Genest is shown threatening Jesse Stone with a revolver equipped with a suppressor (silencer). With the exception of obsolete Russian Nagant M1895, revolvers are not able to be suppressed because of the cylinder/barrel gap allows hot gas, and therefore sound, to escape. The use of a Nagant M1895 by a hit man would be nonsense. It is a collectible gun, ammo is not readily available, and the use of a common auto pistol with common ammo is what a hit man would use.
When Hasty Hathaway shoots Joe Genest in the back, Joe is pointing his revolver at Jesse. The hammer on the revolver is cocked back and Joe has his finger on the trigger. The shock of getting shot would have caused Joe to jerk the trigger and shoot Jesse. With the hammer pulled back, the trigger would need very little pressure to fire the gun.
When Abby calls Jesse in the morning and says that doctor has just told her about the dog, the dog is clearly still breathing.
The rear-view mirror on Joe Genest's Camaro has been removed.
While Jesse is en route from California to Massachusetts, he stops west of St. Louis and calls his ex-wife from a phone booth outside an Irving gas station. Irving is a Maritime Canada chain, with some outlets in Maine.
Healy tells Jesse that Lou drowned in his car. The crash was obviously non-fatal and the car landed in water too shallow to even cover the bottom of the car, let alone enough to drown Lou.