Other mistake: in the scene where 'Sergeant' Jack Travis is asking to see billy Phelps, he is addressed as a Sergeant, later when Lorna is showing the CCTV footage from the interrogation room, she calls him Lieutenant Jack Travis. Is he a sergeant or a lieutenant? Furthermore, given he is a former police officer, he wouldn't be allowed near the station, let alone be allowed to interrogate a suspect in police custody.
Continuity mistake: Just before the end, Riggs and Murtaugh argue in the street. In the background is a cloud of dust and a greenish car driving around. This same car drives the same piece of road 5 seconds later, and another 10 seconds later you hear the same engine/exhaust sound during a close-up (4 passes total if you count the first dust cloud).
Visible crew/equipment: As Riggs and Murtaugh start shooting at the construction site, a shadow of camera equipment can be seen on the pile of wood they are hiding behind.
Visible crew/equipment: Right before the truck carrying ammo explodes near the end of the movie, it comes out of the house as Riggs dives for safety. A man can now be seen who should have been visible in the previous shot - looks like he is lighting a fuse and running... and then boom, the explosion goes off.
Continuity mistake: When Murtaugh and Riggs enter a parking garage to disarm the time bomb in a car's back seat, a No Smoking sign posted on the wall behind Murtaugh becomes obstructed by a vertical pipe and a red warning light between shots. At first the sign is plainly visible, but after Riggs slowly opens the door, the sign's reflection in a window near Murtaugh suddenly reveals the obstructions. (00:03:30)
Other mistake: At the construction site, when the car rolls in empty. Not only is the windshield suddenly tinted, the car is also riddled with about 100 bullet-holes when only 1 or 2 guys fired a few bursts.
Continuity mistake: When Riggs and Sergeant Cole are showing battle wounds at her house, Riggs pulls his pants down to show her the knife wound in his leg from Lethal weapon 2. He is showing her his left leg with a scar on it but it was his right leg that got stabbed.
Continuity mistake: After the end credits roll there is a brief scene similar to the opening, with a building being blown up. Riggs and Murtaugh back out of the area just as the explosion starts and completely leave. There is a high angle shot and a police car appears where they just were. It wasn't there before.
Visible crew/equipment: Right after Riggs saves Rianne's job, he and Murtaugh are driving in Rigg's vehicle. There is a shot looking through the driver's side window. Pay close attention to the reflection the truck makes in the glass on the buildings, you can see the crew and at least two cameras shooting the shot from a rig.
Other mistake: The end credits mis-spell St. Petersburg as "St. Petersberg".