Other mistake: When the arms deal goes wrong by the river in Paris, Larry drives the Audi flat out straight into the tunnel where the bad guys BMW is parked right in the middle, leaving little space to get another car through. Even if he could squeeze the Audi past the other car, there were dead bodies either side that he would have to drive over, as well as crashing into the doors that were left open. This would have done some damage to the Audi at the speed he was going.
Other mistake: Phillip Baker Hall sends Chris Tucker to meet with the FBI immediately after he tells the agent on the phone that he will be sending someone over to them right away. Chris is told by the FBI guy that Jackie Chan's plane arrives in one hour. After Chris picks up Jackie from the airport, he calls his boss to vent his concern. This is supposedly the same day, but both Phillip and Elizabeth Pena are wearing different outfits.
Other mistake: Near the beginning of the movie, the Dude is shopping at Ralph's. He is writing a check, and dates it September 11th, 1991. At the same time he looks up to see a TV with President Bush saying "This aggression (against Kuwait) will not stand." The incident against Kuwait started in the summer/fall of 1990, not 1991. The Stranger (Sam Elliot) and Walter also mention the Gulf War in the present tense.
Other mistake: Gary Sinise is in the hotel hallway and sees various characters going into different rooms. The camera goes over the top of the wall and we see him from above as he enters a room. The camera continues to track into the room perpendicular to the hallway. Eventually the camera passes over the back wall of Sinise's room and we begin to see these other characters in their rooms. This is impossible, these rooms are not behind his but on either side.
Other mistake: When Riggs and Murtaugh are assigned as new captains, they throw their old badges to the Chief and he catches them in his left hand as he grabs the new badges out of the desk draw with his right. In the next shot where he passes them the new badges, he is not shown to have swapped the badges over, so essentially he passed the old ones back to them.
Other mistake: Before the job, in the car, Don Cheadle, in the back seat, hands out a hacksaw, a ratchet and a pump-action shotgun, which he pumps before handing it over. The man taking the shotgun immediately pumps it again, which means it's been pumped twice, and a cartridge should have been ejected, but it wasn't. Or the gun's empty, in which case there was no point pumping it once, let alone twice.kh1616
Other mistake: When Mike loses his bankroll to KGB, he's wearing sweaters/jackets, so it's obviously cold out. 9 months later, he is driving a truck for Knish and wearing cold weather attire. It appears to be a month or so before the WSOP, which at the time was held in late April through May, and at the Judge's game, they indicate he may be an intern for one of them during the summer. So at this time it has to be March/April. 9 months earlier would be July/August, no reason to be wearing winter clothes.