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.