Plot hole: One of the children is a witness that saw the man that planted the bomb in Dixie's house. He is said by a policeman to have been playing 'under the porch' and was close enough to make-out the Special Forces tatoo on the bomber's arm. Problem is, Dixie's house had no porch of any kind, and any other home's porch would've placed him too far to see such a small tatoo so confidently.
Plot hole: Before Riggs, Murtaugh, and Rianne enter the disco after they have killed or chased away their torturers, a man is casually leaning at the bar, with his hands folded in front and moving with the music. When the three protagonists come running through the door he immediately turns around and points a gun at them which apparently he was holding in his hand. One should expect that, in a public disco, even the bad guys keep their guns somewhat better hidden than just in their folded hands when they are not aware of any immediate danger. Furthermore, even the guests close to the bar don't hear the shot when Riggs shoots that guy, even though the music is not loud enough to cover the gunshot.