When Riggs and Murtaugh discover that most of the cargo inside the container is money, Murtaugh notes that "...they're all $1,000.00 bills." Presuming that the movie is set in 1989, the year of its release (see trivia), all denominations of US currency above $100.00 had been withdrawn from circulation for twenty years. Large denomination bills are now mostly in the hands of collectors and dealers. The huge quantity of such large bills would immediately draw suspicion no matter what their source. Part of the reason for the withdrawal was because the large denominations were not widely used enough; other motives include making it more difficult for criminal traffic in large amounts of currency, just the sort of situation depicted in the film. In 1989, there were approximately 220,000 $1,000 bills still being used, considerably fewer than the number of bills on the pallets.
In the opening pursuit scene, the police unit call signs are given as 20W15 (Riggs & Murtaugh) & 20W12. LAPD unit call signs consist of the Division number, then a unit type letter (W to indicate detectives), then the specific unit or patrol area number. LAPD Division 20 is Olympic Division, which came into existence in 2009, 20 years after the movie.
Immediately before the first viewing of Rianne's commercial, when Carrie and the rest of the Murtaugh family are admonishing Roger for eating tuna, Carrie mouths the "Daddy killed Flipper" twice, though in the audio, she says, "you can't eat tuna" the first time, and "Daddy killed Flipper" second.
Obviously, the subplot involving Leo Getz (Joe Pesci) was about protection for his money laundering against the South Africans. In spite of this, he enters the South African counsulate with Murtaugh, offering a diversion for Riggs to enter. This is making a spectacle of himself in front of the very people he means to avoid.
On the Alba Varden, Riggs empties a full clip into a crewmember, calling out the names of police officers who've died. A bullet wound appears on the chest of the crewman for each name but with his final shot, delivered at point blank range, the crewman's chest is clean.
When Murtaugh and Riggs are looking at the money in the cargo container the money is on wooden pallets, but when they break through the doors with the car and the money goes flying there are no pallets.
When Arjen shows Murtaugh's file to Pieter, the DOB states 5-15-45, which would make Murtaugh 44 at the time the film was released. However, Murtaugh was celebrating his 50th birthday in the first film in '86, so assuming the release date is "film canon", his DOB should be in 1936, making him
53. Murtaugh also states that he will retire at 52, which can't possibly make him 53 years old in this movie.
During the series of scenes involving Riggs and Rika in bed, the officers getting murdered one-by-one, the captain and the police running frantic as a result of the officers' murders and Murtaugh and Leo at Leo's apartment, the time line constantly jumps back and forth between day and night.
The diplomat who steals the tow truck activates the tray when Riggs attacks him through the rear window, causing Riggs to flee to the roof to avoid being crushed. As soon as he is on the roof, the tray suddenly stops moving and is then back in its original position for the rest of the chase.
When Murtaugh is watching the home video, and later during the fight, there is clearly daylight coming through the front windows. However, when he goes outside minutes later to check on Leo, it's night.
While Murtaugh is telling his fellow officers when the commercial will be on TV, the female officer behind him is leaning against the glass behind him. In the next shot, she is standing straight up and not leaning against the glass.
When Riggs shoots the gunman and shouts out the names of Rika and all the officers who were murdered with each shot, he fires a total of 19 rounds without reloading (not counting the shot he fired a second earlier at another gunman). A standard-issue Beretta only holds 15 rounds per magazine, so it would be impossible to fire 19-20 rounds without reloading.
When Riggs is on the back of the tow truck and drops his gun onto the road, there is a white fence on the left-hand side of the road. A moment later when Leo gets out of the car and grabs the gun, there is no white fence. This part has obviously been filmed in a different area.
When Murtaugh attends to Riggs after he has been shot in the cargo area, police cars are shown driving across the bridge above the Alba Varden. In this shot the sky is pitch black, but is much lighter two minutes later when the credits are rolling.
There are at least seven officers with Riggs and Murtaugh when they surround the BMW after it crashes, yet it is obvious towards the end of the pursuit that there are not enough officers in each car to make up this number. There are three patrol cars with one officer in each, plus a motorcycle cop, and the officer in the car the BMW hits before flipping (who does not appear to get out after-wards). At best this is five officers.
Murtaugh pulls up right behind the pool guy's truck on the first visit to the stilt house. Later, when he and Leo get in to chase Riggs and the tow truck, the wagon is now some distance back from the pick-up to allow him to pull out without reversing.
The female detective calls Riggs to inform him of Murtaugh's disappearance, and identifies herself as "Collins". However, in the rest of the film (and the end credits), she is identified as Megan Shapiro and Collins is the detective played by Grand L. Bush, who in fact is Detective Boyette from the first film.
When the boys go to pick up Leo from his hotel they walk through the pool area, a woman in a pink swimsuit gets out of the pool. The very next shot you can see she is back in the water and getting out again.
When Murtaugh and Riggs are looking at the money in the cargo container the money is on wooden pallets,the pallets are turned sideways, the "forks" of a forklift would not be able to lift and/or stack them in the way they are and in the confines of a container.
On the Alba Varden, just before Riggs gets hit in the leg by a knife, a moving shadow likely to be from movie equipment, can be seen on the large orange container next to Riggs on the right of screen. (It is not the shadow of Riggs.)
When Riggs is climbing out the water after removing the straight-jacket, you can see the lights shining from under the water, used to make it easier or possible to see Riggs and his "girlfriend" when they were under the water.
People with diplomatic immunity do not have automatic carte-blanche to commit any crime without punishment. If a person with diplomatic immunity commits a crime, law enforcement has to contact the host country, then the diplomat either has his immunity revoked for trial or gets deported back to his/her own country to face consequences there. Arjen Rudd would certainly face (at best) life in prison after shooting a cop in cold blood: the South African government would give him up rather than face an international incident.
In the scene in which Riggs and Murtaugh drive the car out of shipping container, it is highly unlikely that the vehicle would have had enough power to push through multiple pallets of money, easily weighing at least 500 pounds each, *and* break though the heavy, locked, steel doors of the cargo container, from a standing position. This would require the vehicle to have a "running start", and it simply didn't have the room inside the container.
Arjen Rudd claims throughout the movie that he has diplomatic immunity. Rudd works for a consulate - not an embassy - and therefore would have consular immunity; this is similar to, but weaker than, diplomatic immunity (e.g., it generally does not provide immunity from arrest/prosecution).
When Murtaugh and Riggs are looking at the money in the cargo container the money is on wooden pallets,the pallets are turned sideways, the "forks" of a forklift would not be able to lift and/or stack them in the way they are and in the confines of a container
After the car is driven out of the cargo container and lands in the water with all the money (at the end of the film) As Riggs and Murtaugh run to the end of the hanging container armed with machine pistols, there are already 2 conveniently tied off hanging ropes for our heroes to repel down to the ship.
When Murtaugh is showing Riggs the new addition to his home, the contractor fires his pneumatic nail gun. In all scenes, it can clearly be seen that there is no air hose attached to the gun, seemingly making it impossible for it to work. However, some nail guns are powered by batteries, CO2 gas, or even blank cartridges. The nail gun used doesn't appear to have the 'air hose' connection.
When Vorstedt reveals to Riggs that he was the one who mistakenly killed his wife, the whole subplot makes very little sense. If the "contract" was on Riggs' life, it's unlikely that Vorstedt would just drop it after the mistake and fail to proceed to kill Riggs himself. It's also unlikely for a character like Riggs to give up a hot case even after a grave loss. Even if he was pulled off the case, someone else in the PD would have picked it up after him.
When Murtaugh is showing Riggs his hobby room, they are supposed to be surprised when the carpenter fires the nail gun. However, moments before he fires it, they both have their hands on their respective guns, ready to react when they hear the 'shot'.
When Riggs pulls Murtaugh out of the toilet and into the bathtub just before the toilet explodes, if you look extremely carefully, you can see Murtaugh is wearing dark pink briefs, even though he should have been naked from the waist down for obvious reasons.
On the Alba Varden, just after Vorstedt throws the knife at Riggs and they begin fighting, there is a cut to Murtaugh shooting another diplomat, then when it cuts back to the fight between Riggs and Vorstedt they are in the darkness where Vorstedt had been hiding when he threw the knife at Riggs, and in the background is the large orange container which Riggs was standing near when the knife hit him in the leg. The distance between Riggs and Vorstedt would have been to far for Vorstedt to have thrown the knife at Riggs, it would have barely reached him.
The "Liquid Nitrogen" brought in by the bomb squad bring in during the bathroom bomb sequence is just dry ice in water in a Pyrex measuring cup. Real liquid nitrogen has to be kept in a special container to remain a liquid so if they tried pouring it in a room temp open air container it would revert to gas almost instantly and be useless.