At the gun club, when Axel is offering his grooming services to Karla Fry, she is shown firing a revolver. But the sound effects of ejected shells hitting the floor after each shot can be heard. Revolvers don't eject their shells.
When Axel, Billy, & Taggart arrive at the 385 strip club, the Maitre d' stops Axel and looks at Billy and Taggart and asks, "And who are those awful-!", then Axel cuts him off. The last word, "awful" was obviously dubbed, as it becomes louder than the rest of the sentence. And is you read his lips, he says, "And who are those people?"
When in the cement trunk, Foley asks Rosewood if the brakes work on "this thing" Rosewood replies by saying " I don't know, I haven't tried them yet." When Taggart is chasing after the cement truck, it brakes to make a right turn. So in fact, he has tried them, and they do work.
In the opening sequence, the limo in which Karla and the robbers arrive in is seen having two different license plates. In the first shot, the front plate reads 'DENT', but as the scene progresses, the plate simply says '77'.
When the cop car is taking a sharp left turn during a chase, the red light falls from the roof and hangs from a cable. The passenger in the car picks it up half way and in the very next shot it is on the roof perfectly in place. Also, the same shot (of the unmarked police car taking a sharp turn with the red light dangling on its wire) is used again during a later chase.
During the opening credits, Axel Foley begins driving a Ferrari 328GTS with the targa top removed. When he pulls into the alley, the car is a Ferrari 308GTS with the targa top in place. The car remains a 308 in all of the high-performance shots on the streets of Detroit. When he pulls up to the bar where he offers to buy 2000 American Express cards, the car is again a Ferrari 328GTS, except the targa top is now in place.
When Taggart yells at Axel to get out of the pool, he is wearing his sunglasses and is holding his cigar in his right hand, but when Taggart falls into the pool, his sunglasses have disappeared and his cigar is now in his mouth.
When Rosewood pulls up to the racetrack, both doors on the right side of the car are open. However, in the next shot, we see Taggart exit out of the vehicle from the left side and the door on the right side is now closed.
In the scene where Brigitte Nielsen is shooting in the Beverly hills shooting club and talking to Eddie Murphy. She fires a rifle then an automatic pistol last she picks up a 6 shot revolver not only does she fire 11 shot with out reloading but you can hear shells dropping on the floor (revolvers don't eject shells).
When Foley cracks the code of Charles Cain in the car, they do a left turn and the light on the roof of the car falls and is hanging by the cable. In the next shot it is back on the roof. Also, during the sharp left turn that makes the light come off the roof, Foley can be seen riding in the passenger seat. In the next shot he's sitting in the back seat.
During the shootout at 385 North, the tail lights of the Camaro are shot out several times, and both tail light's red crystals are broken. In the following cut, the red crystal is seen being shot out again.
When the Cadillac backs up in the driveway to let the armored van pass, it clearly drives off afterward at speed. In the next shot, when Billy hits it with the cement truck, the Cadillac is now stopped side-on in the middle of the road.
There is a car behind Axel right before he pulls into a driveway to turn around and go speak to the building inspector at the house that is being redone. However, when he pulls into the driveway to turn around, the car behind Axel is gone.
When we first see Karla Fry following Bogomil early in the film her Mercedes convertible has a blue on white California 'Sunrise' license plate. In the next shot when she is pulled off to the curve with the cars hood open the plates have changed to the old yellow on blue California type.
Immediately after the cement truck chase when Foley and Rosewood located the armored car abandoned on the side of the road, Foley spots some tire tracks from the getaway car. If you look at his shoes, you can see they are muddy as he walks to the tire tracks. In the next scene however, when Foley locates more tracks (just before Taggart shows up), you see his shoes are no longer muddy.
When racing to the City Depository, the magnetic red lamp falls off the roof of Billy's unmarked squad car while making a sharp turn to its left. In the very next scene, the light is still on the car's roof.
The license plate on Rosewood and Taggert's police car is 2GAT123. This car is completely wrecked while en route to City Deposit. Later in the movie, while en route to Empyrean Fields, the same license plate is seen on their new car.
At the gun club, Axel shoots three times, yet his semi-automatic pistol - which should hold two or three times that many rounds depending upon model - is empty, as is shown by the slide being in the back/empty position.
The Captain gets chewed out by the Police Chief for involving the FBI in solving "The Alphabet Crimes." But the Diamond Store robbery is the "A" crime; i.e. the first and only Crime. How does anyone know (at this point in the movie) that there are going to be further "Alphabet Crimes"?
The "bad guy", Dent, is known as the "Alphabet Bandit" because the crimes his crew commit occur at locations with alphabetical names. But he becomes known as the Alphabet Bandit after just one crime, the "A" crime. That doesn't make sense.
When Axel calls Jan from Sidney Bernstein's office, she mentions that her dad was up and around. If that was the case, why didn't Axel, Taggart and Rosewood just go to him to find out what he knew and therefore could have captured Dent & company even before they could hold up the race track.
During the scene where Axel first visits the gun club, it is daytime. Out the window of the scene in the office where Dent and Cain are discussing killing Foley, you can see past the bushes that it is dark outside, and a daylight balanced light is providing the "sun" beam through the window.
When Axel bends down behind a car at the oil fields to check out the color of the dirt, you can see it is obviously spread around just around the area behind the car. No where else in the parking lot is there red dirt.
When Axel, Rosewood and Taggart are running the matchbox's fingerprint through the computer downtown, it identifies the print as belonging to Cain and prints out his dossier. Taggart takes the printout and read aloud "Charles Cain... used to be Charles Campos". If you look at the dossier carefully, it only identifies him as "Charles Campos" and there is no reference or mention to his alias as "Charles Cain" anywhere on the printout.
While en route to the City Depository, at the construction area, Billy spins the car around and we hear a crash, and Taggart shouting, "Shit!", and then they all jump out of the car as it is totaled. Yet the car does not actually hit anything.
When Axel calls Detroit from Billy's apartment, He is told it is 1AM. When they leave the apartment just a few minutes later, Taggart says it is 11PM. Detroit is in the eastern time zone, and LA in the Pacific, therefore there should be a three hour difference in the time. The only possible explanation is that it is the morning that daylight saving time ends, thus the clock has just 'fallen back' in Detroit. However, the time frame of the movie does not allow for this.