Just after Hank trashes the car in the handicapped space at the convenience store, only Hank and Irene are in the car driving away. Whitey is missing. A couple of shots later, he is again in the back seat.
The ketchup bottle sitting on the grill (at the kid's birthday pool party) is a squeezable plastic 'flip-top' ketchup dispenser with a distinctly modern label. This particular ketchup bottle did not exist in the mid-1980s.
A scene showing Charlie return home to his teen aged boys attempting to build a small airplane, shows, in the background, a mid 1990s Oldsmobile Achieva driving by but the scene takes place in the late '80s.
Shonte Jr. complains about Pluto being a planet, saying that no planet has an elliptical orbit. All of the planets have elliptical orbits; Pluto's orbit is only more eccentric, and isn't in the same plane as the rest of the Solar System.
When Charlie and Irene leave for New York, the Colonel and his assistant are talking about him being a liability. The assistant says "But Captain, Police Work is Charlie's life...", incorrectly addressing the Colonel as a Captain.
The Ford LTD 2-door belonging to the "Barber Shop Car Owner" is a 1979 to 1982 model when it's parked out on the street. However, it changes to a 1983-1987 model when Hank crashes it through the window; the grille changes completely.
During the scene where Charlie is being bandaged after having his thumb shot off, the RIPD police cars have blue light bars. During the scene of the road block for Irene, the RIPD police cars have red light bars.
When the cow moves again after Charlie shot it in the head several times, he throws the gun out of camera shot. When the camera shows Charlie wrestling with the cow, the gun mysteriously appears next to the cow's head.
When Charlie is talking with the little girl, as she says her line "My dad says you're a joke..." two people can be seen walking past behind Charlie. We cut to a close-up of Charlie sighing in exasperation, and the same two people walk past behind him again.
In the last scene when looking for Charlie's thumb in the water, Whitey puts his head in the water (the snorkel is not in his mouth). From the underwater camera, the snorkel is in Whitey's mouth. When Whitey lifts his from the water, the snorkel once again is not in his mouth.
Near the end of the film, we see Irene and her ex-boss on a deteriorated wooden bridge. The gaps in the bridge's planking are spanned by two parallel boards. However, moments later when Charlie crosses the same bridge, the gaps are spanned only by single planks.
The length of the white picket fence, between Charlie's house and his rude neighbors, changes several times throughout the movie. Sometimes it appears to reach close to the road, other times it is more flush with the houses.
When Charlie first loads up Irene on the back of his motorcycle and takes off, the first highway shot bounces and the front wheel of the motorcycle can be seen clearly mot even turning, indicating the bike is on a trailer. The vast majority of cycle shots make the bike look this same way, like its on a trailer.
Before they make the first train stop, the train conductor announces they will be stopping at Providence, Rhode Island. But, the scene is filmed in Burlington, Vermont at One Main Street's train station. You can see a sign that says "Burlington" along with the distinctive addresses seen and license plates.
Scenes of Charlie/Hank's house were shot in the Bonnet Shores neighborhood, in the town of Narragansett. At one point, Charlie/Hank leaves his house for a drive (I think to work). The very next shot shows him driving west over the Newport Bridge, which is the incorrect direction if he's leaving from Narragansett.
Charlie's diagnosis of "advanced delusionary schizophrenia with involuntary narcissistic rage" is incorrect. Schizophrenia causes delusions and hallucinations with paranoia. Many people used to believe that schizophrenia resulted in multiple personalities, but this is not the case. He should have been diagnosed with dissociative identity disorder (also known as multiple personality disorder). Further, there is no medication used to treat multiple personalities, although some medications can be used for other symptoms (such as anxiety and depression) that accompany the condition. Treatment of DID involves years of psychotherapy - the disorder cannot be cured by taking a pill as portrayed in the film.