Other mistake: When Riggs kills the guy who murdered his wife by dropping that cargo crate on him it's obvious the crate has no bottom and it falls around him, not least because the body's height doesn't change as the crate falls, there's no sign of impact or crushing, he just stays perfectly upright as it hits the ground. (01:39:25)
Other mistake: During the "high speed chase," Murtaugh stops the car so that Leo can retrieve Riggs' dropped gun from the side of the road. He picks it up and runs back to the car. Murtaugh says, "Give me that," and takes the gun from Leo. But, Murtaugh, being in the driver's seat, wouldn't be able to reach over the passenger seat and a foot or so outside of the car to grab the gun from Leo. It looks like someone in the passenger's seat just reached out and grabbed it.