When Axel is thrown through the front window of Maitland's office building he is in the sun. When the police pull up, he is in the shade. As the scene goes back and forth between the two angles, Axel goes from being in the sun to the shade, then back to the sun.
When the goon is thrown over the buffet table at the Harrow club, his face lands in some sliced oranges. In the next shot, cream and strawberries are on his face.
When the henchmen run out after seeing the police on the monitors, their shoulder holsters disappear and reappear.
During cigarette truck chase, the plate on the truck's hood, from the crash with a vegetable truck, disappears after the bus breaks, the reappears in the next scene.
Foley and Taggart run past the windows of Maitland's mansion,which had been shot out. In later scenes, the glass is back in place.
Maitland's German bonds are incorrectly labeled "10,000 Mark". The official name for West German currency was "Deutsche Mark." East Germany used "Mark", but bonds did not exist there. In German the comma functions like an American or British decimal point, so the bonds were worth 10 marks.
In the pool scene, the hustler says "8 ball, corner pocket, 2 cushions." The 8 ball made contact with cushions three times before falling into the pocket. Mikey won his bet.
Police drug dogs would not be fooled by cocaine shipped in coffee grounds. They would smell the drugs and the coffee at the same time. Even a few specks of powder on the outside of the crate would alert the dog.
When Foley first enters the Detroit police station, the name on the door he goes through is misspelled "INVESTIGATON OPERATIONS DIVISION".
In the opening chase scene, the Detroit police cars have a single bubble siren. Only Michigan State Police cars are set up this way. Detroit has a two side-by-side siren set up.
While Rosewood and Taggart wait on Foley to come back to the hotel, Taggart drinks coffee from Dunkin' Donuts. In 1984, Dunkin' Donuts had several dozen California locations. They were phased out in the 1990s.
When Axel throws Maitland's henchman over the buffet table at The Harrow Club, it's clearly a big, burly stunt double doing the throwing.
During the opening chase, Axel is a few inches taller, with different hair and more muscular arms. He's clearly a stunt double.
At Maitland's house, after Taggart collapses on the grass after being shot at for the first time, holes in the grass indicating where the bullets will "hit" are clearly visible.
When Jenny and Axel go into the warehouse for the second time, the door is unlocked and open before Jenny even inserts the key. She never even turns the doorknob, yet the door opens.
Most of the cops' revolvers have no bullets.
After the shooting is done and Foley is sitting outside (after being shot in his right arm) and gets up, his gun in on his back belt. The position of the gun shows it was placed with his right hand which is supposed to be in pain such that he just shot using his left hand.
Axel books into the hotel and his bag is a specific size. When he books out and buys bathrobes for Billy and Taggart, he says that he has three bathrobes in his bag. However, his bag is no larger when he left than when he arrived. Either there were bathrobes in his luggage and the bag was not enlarged or he (being a cop) did not steal the bathrobes.
When Axel is shot by Victor in the arm the round (either .357 or .44 magnum) would have just about taken his arm off and he would have probably bled out. Yet he only has a minor wound.
When Foley walks across a tiled floor in Maitland's mansion, his sneakers make the sound of hard-soled shoes.
After Axel Foley is arrested and the police car pulls up at Beverly Hills police station, the two officers get out. As the officers walk to the rear door to get Foley out, Foley is heard saying, "Officers, if we see any like... movie stars, could y'all stop and point them out, I never seen no shit like that." One officer is heard responding "That's enough talkin', pal.". Throughout this dialogue, the officers are outside the car, while Foley is inside, the windows are up and it is obvious Foley is not talking.
When the police car hits the barrels during the opening chase, it's shown from the inside of the patrol car behind it. In the next exterior shot, the camera is visible in the front seat.
When the cigarette truck smashes into the taxi, crew members are visible on a nearby roof.
As Axel is led into the Beverly Hills Police Department for the first time, the camera crew is reflected in the plate-glass windows in the hallway.
Whenever Victor Maitland's black Mercedes drives past the camera, the crew is reflected in its polished black doors.
In the opening truck chase, just before the shot of the green taxi, a movie camera can be seen mounted inside one of the police cars.
It makes no sense for the villains not to kill Foley after they kill his friend. Foley is a loose end and potential witness. They are unscrupulous career criminals and murderers. If they get caught, they are up for first degree murder anyway.
Somehow after being in prison for a few years and then working in California for months Michael is able to find Axel's apartment in Detroit. Also, the hit men from California are able to easily find the same apartment.
No reason or logic at all is provided for why Maitland kidnaps Jenny after she and Axel find the drugs in the warehouse, especially when he easily could have shot her and Axel under the guise of killing intruders and gotten away with it clean by the police.
After Mikey is killed, Axel drives his Chevy Nova from Detroit to Beverly Hills to investigate the crime, a distance of about 2,300 miles. When he enters Victor Maitland's office, he says that Mikey visited him a couple days ago, meaning Axel would have to have covered 2,300 miles in 24 hours by car, an impossible feat when you consider that fuel and rest stops are required.
It makes no sense for inspector Todd to consider the killers of Foley's friend to be professional hit men because they left Foley alive. Leaving a live witness and lose end around should in fact make the inspector assume the exact opposite.
In the strip club, Axel jokes that if he drinks club soda, he'll throw up, but he ordered a scotch and soda moments earlier.