Continuity mistake: When Riggs is hanging from the tree, his hands are tied behind his back. When he falls and lands on his back, his hands are still behind his back. In the next shot of him, his hands are now tied in front of his body, even though he didn't have time to do anything to get his hands there.
Continuity mistake: When Riggs gets loose and frees Murtaugh, Murtaugh has no shoes on and is running after Gideon barefoot. Then the next scene shows Murtaugh walking in the hallway with his shoes on. The next frame that Murtaugh is in shows him again shoeless and hoping that it is water that he is running in. (00:37:12)
Continuity mistake: At the barber shop Murtaugh's son takes his headphones out to listen to his dad while he's talking to him. Right after there is a quick camera angle change and you can see in the mirror his son has his left headphone back in his ear. The headphone appears and disappears throughout the scene. (00:00:15 - 00:01:00)
Continuity mistake: When Roger is playing chess with his father-in-law, the pieces on the board keep changing in each shot, and too drastically to be moves done off screen. For example, at first Roger's left rook is not on its starting position but in other shots it is.