Continuity mistake: When Governor Tracy is filming an ad, a wide shot shows there's nothing on the lawn in front of her. When she finishes her speech and the shot changes, the crew and equipment suddenly appear. (00:14:40)
Continuity mistake: Chris Farley and David Spade are driving in a borrowed police car. When the camera is on Spade, the window is not open, then it is open a bit, then it is closed again.
Continuity mistake: After Spade gets foamed, in the scenes to follow, the foam stains change many times, in addition, he has his coat on, then off, then on again in different seems, and the coat never seems to have any foam either.
Continuity mistake: When Steve gets foamed by the farm boys, he has tan trousers on. When he goes back to Mike, his pants are dark. When he meets Mike, his trousers are tan again.
Continuity mistake: Near the end when Mike is on top of Governor Tracey, the camera pans to a wide shot and there's no sign behind the people on the stage. In the newspaper picture of Mike on top of her, there's now a sign behind the people.
Continuity mistake: When the boulder is coming down, the front door is open. When we get a shot of the front of the cabin, the door is now closed. However, the doorknob switches from being on the left to being on the right. We also see there is nothing hanging from the porch roof. Before Mike and Steve crash through, we see the front again and the doorknob is back to the left and there's a metal star hanging from the porch roof.
Continuity mistake: When the boulder hits the cabin and Mike falls out the front door, he's rolling, almost off the door, and on his side, with his back close to the rocks. There also is nothing on the back of the door. When it cuts to the close up, Mike is now face down on the door completely, with a dartboard on the door.
Continuity mistake: When Mike is playing football on the field, he scores a touchdown, and throws the football down. Then it cuts away to the kids complaining, then back to Mike, and the lost football is in his hand. It cuts to a larger view of the scene, and where's the football? The camera cuts away again, and then back to Mike and his team. The football is once again in Mike's hand.
Continuity mistake: Near the end of the movie, while at the Governor's mansion, Drake Savage (played by Gary Busey) is in a tree with a rocket launcher. He jumps out of the tree and lands without the rocket launcher. In the next scene, he jumps onto the stage and he has the rocket launcher, which he left in the tree.
Continuity mistake: When Chris Farley is at the top of the hill, he then slips and falls for a little while. He finally gets to a place to stand up, and his blue shirt is covered in dirt. He then falls again, and when he reaches the bottom, he stands up, and his blue shirt is completely clean.
Continuity mistake: When Chris Farley helps the old couple in the grocery store parking lot, he slams the trunk closed and his tie falls out of the trunk. Then the scene cuts to the old couple driving off and dragging him behind.
Continuity mistake: When Chris Farley falls from the TV van anntena thing he is going to land on his left shoulder but in the scene where he hits the ground he goes down on his right shoulder.
Continuity mistake: When Governor Tracy is chopping down the tree, we see the pre-made cuts (that are suppose to be there). After her 2nd chop the shot changes to her family, but when it goes back to her, there's a new notch in the tree and it's not from her chopping as we don't hear her chopping. When it cuts to the tree the final time, after she says "don't let anyone tell you your job is easy", there are more chop marks that aren't from her.
Continuity mistake: When the cabin was struck by the boulder it was tilted downwards making Steve and Mike fall out the front window and door. As Steve and Mike were leaving to go watch the debate at Drake's bus, both guys walked uphill to leave by the front door.
Continuity mistake: When Drake sneaks up on Steve while he is urinating on the tree, he turns Steve around, and as happens in many films when someone is interrupted while urinating, his genitals are magically back in his pants. You can then hear Steve urinate on the ground a couple times as Drake continues to intimidate him, which wouldn't be possible if his genitals were back in his pants.
Continuity mistake: When Mike and Al are on the football field talking, after the truck incident, they're a couple feet away from the "50" and start walking back to the cars, away from the "50" and get to about the 44-yd line. After Roger honks the horn, Mike and Al are now back to around the 50-yd line and next to the "50." And they're closer to the "50" then the first shot.
Continuity mistake: When Mike is talking about seeing his brother while Steve is asleep, you see the Playpen magazine sticking out from under his pillow, on top of a 2nd magazine. When Mike approaches him, the Playpen magazine is under the covers next to Steve and there's only one magazine under the pillow.
Answer: A major police department would probably not allow modifications to an official vehicle, even if it was assigned permanently to a particular officer, due to safety or insurance concerns. That said, many departments do use high performance or exotic vehicles seized during crimes under various forfeiture laws. Most times these are for promotional purposes, but I do know of a Florida department that used a souped-up Dodge Hemi-Charger painted in standard department livery for traffic enforcement.