Plot hole: When the armored guy is propelled under the tanker trailer, his backpack explodes. That blast can not have been large enough to lift the entire trailer through the air. The trailer never explodes itself, and if it did, the tank itself would have torn apart and the frame beneath would have stayed on the ground, pushed down by that blast above. (Oh, and there's no such "safety feature" that is intended to launch a trailer in the air in case of an accident.) (00:05:00)
Plot hole: When Riggs, Murtaugh, Lorna and the others are tied up and lying on the floor of the burning house, they can't stop coughing. However, the bad guys (who are also in the burning house) are just standing around laughing, wouldn't you think that they would be inhaling smoke also?
Answer: It was put in the film to introduce the concept of Rianne and Lorna being pregnant and to bring in the joke about the news article about Roger, not to mention giving the film an action-heavy opening.