Continuity mistake: In the chase on the grand prix circuit, the weather continually changes from wet to dry and back again.
There Goes the Neighborhood - S1-E4
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 Riggs and Palmer fall through the roof and onto the bed, the debris under them changes. In the final shot there's a huge piece of the ceiling in between and under them that wasn't in the previous shots.
Continuity mistake: When Riggs is talking to Agent Palmer about being hungry, he's holding one red folder. When he asks if she was going to eat, he sets the folder down. In the next shot, he's holding a folder again.
Continuity mistake: When Riggs throws the water bottle to Leo, he catches it with his left hand, in the next shot he's holding the bottle in his right hand.
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)