Some dialog, including the opening narration, refers to local law enforcement as the sheriff's department and to Sergeant Goldhaver as a sheriff's deputy, but other dialog, and all of the signs at the station as well as the patches on Goldhaver and Lieutenant Mattson's sleeves say "Police".
Vincent and Goldhaver end up in a shoot out with the aliens at the greenhouse. Goldhaver hits the ground and gets filthy with dirt. A few moments later, when the Invaders are defeated, Goldhaver's uniform has just a few dust marks.
When David and Sgt. Ernie are talking in the police car on their way to the courthouse (and a similar later scene) the interior shot of them in the car shows a shiny black and chrome Ford Galaxie. In the exterior shots, they get out of the car - and the interior of that supposed same car shows a white plastic trim pillared sedan and white headliner, seconds later.
During the fight in the diner, the stunt doubles for Roy Thinnes and Gene Hackman are obviously not Thinnes and Hackman. This is especially obvious in the case of Hackman who is balding while his double has a full head of hair.
The spores growing into alien infants in the hothouse appear to be glistening but it is all too easy to tell why: they are wrapped in cellophane.