Continuity mistake: Right after Riggs tells Murtaugh how he is going to be a distraction for the man shooting fire, Murtaugh starts taking off his jacket in one angle, but in the reverse shot looking toward him, he has it back on and isn't touching it. (00:04:05)
Continuity mistake: During the car chase involving the car driven by the Chinese guy, Murtaugh, and the mobile home, the two cars slide against each other and the right wing mirror on Murtaugh's car is completely wrecked. Once the two cars are separated the wing mirror has miraculously repaired itself. The left wing mirror also does a disappearing / reappearing trick.
Continuity mistake: In the scene near the end of the film when Murtaugh shoots at Wah Sing Ku and mistakenly kills the last of the four fathers, you can clearly hear an empty shell casing hit the floor, although he is using a revolver, which do not spit out the empty shells as they are fired.
Continuity mistake: In the scene where Riggs throws the table leg at the man's car, the table leg makes a hole and the glass around cracks. Each time the camera focuses on the car the amount of glass that has cracked has changed.
Continuity mistake: At the end of the movie when Riggs, Murtaugh and the other two cops enter the garage where the Triad chief is buying the four fathers' freedom whe can clearly hear the hard rain outside, but the car that they're driving is completely dry - maybe they had a very big umbrella!
Continuity mistake: After Riggs shoots the human tank's napalm valve and he goes flying under the tanker truck, Riggs hops over the hood of the car he's behind. In the next shot, he and Murtaugh are running away from the falling tanker as if Riggs had never moved.
Continuity mistake: When the car launches towards the office block you can clearly see the rollcage and missing passengers.
Continuity mistake: In the scene where Riggs and Murtaugh drive a car through an office, you see Riggs floor the car in one shot, and when they show a view of the car you can see the brake lights are on.
Continuity mistake: During the gunfight with the armored man, more and more bullet holes continue to appear on Riggs and Murtaugh's side of the car which is facing away from the armored man with the gun. And in one brief scene from the armored mans view, there are no bullet holes on the side of the car which he had fired at and hit several times.
Continuity mistake: When Riggs is on the table and jumps into the moving car, the table is run over by another car. A few seconds later you can clearly see the table still attatched to the plastic.
Continuity mistake: More geographical problems: During the scene filmed on a supposed L.A. highway where Riggs is on a table loosely connected to a semi, the Luxor Hotel in Las Vegas is seen in the background.
Continuity mistake: Near the end when Butters is shot, Murtaugh is holding Butters' head up, you can see Murtaugh's tie down on his chest and in the next shot it's over his shoulder, but next shot the tie hangs down again.
Continuity mistake: Right before the highway scene, the distant mountains are green and lush, but when they get onto the highway, the mountains become close and desert-like. This is because this scene was done on the empty, brand-new I-215 in Las Vegas.
Continuity mistake: When Riggs suggests that Murtaugh take his clothes off to distract the gunman, Murtaugh's tie suddenly drops and his collar is undone. In the next shot his tie and collar are done up again.
Continuity mistake: Near the beginning, when the tanker trailer is blown, you can see where each of the charges are placed the moment it blows as well as see the rear wheel of the tanker mechanically fold under.
Continuity mistake: When Riggs is hanging off the roof and the others are trying to move a dumpster for him to drop into, the handcuffed Chinese waiter is trying to help. A shot from the top shows the waiter pushing the dumpster with his (outstretched) leg, but a split second later, a shot from the side, he has his back to the dumpster.
Continuity mistake: The scene on the highway where Riggs and Murtaugh are chasing the black Mercedes in their Pontiac, the windows on the Mercedes repeatedly change between tinted and non-tinted.
Continuity mistake: During the mobile home chase, you can see a white car following Murtaugh. In the next shot, when he starts to overtake the mobile home, the car is black.
Continuity mistake: In the trailer chase scene, when Riggs is being dragged by the plastic wrap, it cuts away to a far shot of Riggs on the table. The "plastic" he is holding on to is very obviously a thick metal cable wrapped in saran wrap or something to make it look like plastic.
Continuity mistake: In the scene where Riggs is at his wife's grave, Leo comes along to give him advice. In the scene he was in previously he had cuts across his face. At the cemetery the cuts are gone, then they reappear in the following scene at the hospital.
Answer: It was put in the film to introduce the concept of Rianne and Lorna being pregnant and to bring in the joke about the news article about Roger, not to mention giving the film an action-heavy opening.