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. (00:57:40)
Suggested correction: The rear of Dixie's house is never shown. The house could conceivably have a back porch the kid could have been playing under and the killer could have used the back door.
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. (01:25:20)
Plot hole: There is no way Riggs and Murtaugh would have let Joshua kill the two officers guarding the house, if they were already waiting for him. And if they didn't get to the house first, there certainly would not have been enough time for them to reach the house and leave a message waiting for Joshua in that short space of time. So, were they waiting for him or not, and why let two cops be killed if they were?
Suggested correction: They didn't get to the house before Joshua; they showed up after he killed the two police officers. The note is in a child's handwriting, so it's more likely that Murtaugh called the family to tell them to evacuate the house, and one of his kids left the note.