In the video/theatrical release, in the final battle with Vincent Ludwig, Frank Drebin's chest protector has deflated without reason. (note: the network television broadcast adds a scene in which Ludwig shoots the chest protector, causing it to deflate.)
In the airport, we see a DC-10 (in United Airlines colors) landing, but when Drebin is deplaning, he's getting off a Lockheed L-1011 (in TWA colors).
In the hospital scenes Nordberg has a cast on his right arm and his left arm is fine. In the final scene at the stadium Nordberg's right arm is fine and his left arm is in a cast.
In a close-up of Dr. Alfred, the rear window of the Taurus can be seen smashed before Frank shoots it.
When Drebin is pretending to be the umpire, his mask changes several times from having protective bars in front of eyes to having no bars there.
The mayor incorrectly refers to The Queen as Her Royal Highness. As reigning monarch, she should be referred to as Her Majesty.
Ludwig mentions that the fish in his tank are 'Japanese Fighting Fish'. They are actually Lionfish. There are no actual 'Japanese Fighting Fish'. Siamese Fighting Fish, or bettas, are much smaller and cost much less than Ludwig says.
When Drebin is singing the national anthem, the American flag behind him is in the wrong position. The Union Jack is to the flag's right. US Flag protocol mandates that no flag should be on the American Flag's right (the viewer's left) when flown at the same height.
When Frank is pretending to be the home plate umpire, the first pitch is thrown. The catcher catches it, and everyone stops and looks at him for his call. In reality, if the home plate umpire makes no call and says nothing, it's a ball.
During the intro to the baseball game, the US national colors are shown at "present arms", aka dipped, showing a salute. In actual fact, the flag/colors never dip for any reason.
When Frank Drebin is umpiring the baseball game, a scene shows four Angels players crossing second base during the same play. This is a joke, as the situation is impossible in baseball; even during a grand slam, only three players touch second base. The scoreboard later shows no more than 2 runs scoring in any inning, in keeping with the joke.
The Angels play in Anaheim, not Los Angeles. While the game scenes were filmed at Dodger Stadium, it was identified in dialogue as Anaheim Stadium. This incorrect attribution appears to be a goof, but it is not. Originally, the plan was to have the Dodgers appear but the Dodger organization refused to participate because of the big brawl that occurs on the field near the end of the film. (They even refused to allow Vin Scully to appear in a cameo.) The Dodgers, however, were perfectly fine with renting out the stadium with the stipulation that "Dodger Stadium" must not be visible. The Angels organization had no problem letting their team name be used - and that is why the Angels appear in Dodger Stadium identified as Anaheim Stadium. It was not so much a goof but an unfortunate set of circumstances that left the movie makers no choice.
In the opening scene, Idi Amin is wearing his uniform, even though at this point, he was in exile and it was nearly a decade after he was overthrown. It's likely he secretly kept the uniform to be used for a special secret meeting.
The 1983 Ford LTD Crown Victoria--the car driven by Frank Drebin--was not equipped with airbags. However, this was meant to be a joke/gag.
When they enter the Police Lab, we see the words on the glass door from the inside. "Police" is in reverse, but "Lab" appears as normal - they can't both be right. This is obviously an intentional joke, continuing a running gag from the series (with "Police Squad" written in opposite directions on the door).
Although the baseball stadium is filled to capacity for the Queen's visit to the ballgame, the background view to the outside during the final scene shows the parking lots to be completely empty.
When Drebin is riding in the back seat of the "driver's ed" car, the gear shift stays in the same position even while the car is reversing.
After Nordberg has been sent careening down the steps of the stadium by Drebin, he hits the fence and flies out of his wheelchair. The gas from the gas cannon that fired his stunt dummy out of the chair can be clearly seen.
During the baseball players fight, Reggie Jackson can be seen already robotic walking in the background towards third base. Moments later, only then is he subject to "secondary-induced hypnosis" and robotic walks over to third base to retrieve the hidden gun.
Enrico Pallazzo is somewhat heavier and slightly shorter than Frank, yet his tuxedo fits Frank perfectly.
When Frank hits the trash cans in front of the police station, the airbags deploy and the second "airbag" pushes the gear selector up, causing the car to roll down the hill. In a car with an automatic transmission, the selector must be moved down to take the car out of 'park'.
Ludwig's 'mind control' remote device is still able to work (when a marching person steps on it) after it was --flattened by a steamroller.
When Frank and Ed get in the car at the airport, Ed removes then throws his hat in the rear deck of the car. Arriving at "The Hospital", the hat is gone.
When the driving instructor tells Stephanie to "extend your middle finger" he mouths an expletive instead. More than likely the original audio was voiced over so the movie could keep its PG-13 rating.
(At about 36 minutes) Frank enters his apartment and cartwheels behind the bed. When he pushes down on the bed to get to his feet, the stuntman who actually performed the cartwheel can be seen on the floor behind Frank.
In the hospital, when Drebin climbs over Nordberg to go after Dr. Alfred, a microphone wire is visible coming from under O.J. Simpson's hospital gown.
Crew reflected in the side of the Taurus as it tries to stop before hitting the petrol tanker.
In the opening sequence, as the "car roof" and siren enters the house, the camera's shadow is visible.
The opening panoramic shot of the city labeled as "Beirut" is actually Cairo, Egypt, as seen from the roof of mosque of Ibn Tulun.
Even given that the movie is a satire of police ineptitude, it is unlikely absolutely no other cops would have been in on Nordberg's undercover operation and able to clear his name.
Comparing the size of the cake of the Queen and the piece Drebin received, there wouldn't have been enough to go around every guest in the banquet hall.
The British National Anthem is played as HM the Queen is entering the baseball stadium, but the Queen keeps walking. In reality, she always stands still (and to attention) when the anthem is played.
When the Queen enters the reception at the hotel, the Mayor introduces her as "Her Royal Highness..." but the proper form of address for the Queen is "Her Majesty..."
The mayor states that the city is presenting the queen with a "Revolutionary War musket," but the firearm Ludwig holds up is clearly a rifle, not a smoothbore musket.
When Ed looks at the picture in the hospital, he says "I LUV YOU, out of Caracas. A Panamanian ship.." Caracas is in Venezuela, not Panama, but he could mean it was a Panamanian ship whose last port was Caracas.. However, when the picture is shown to the audience, there is no indication of the ship's registry (no visible flag, crest, or wording). Ed would have no way of knowing that the ship was from Caracas.