Continuity: In the hockey game, the teams playing are the Los Angeles Kings and the Toronto Maple Leafs. You can notice the real logos when the camera is away from the action. When it gets closer, though (probably because of copyrights), the maple leaf is turned into a spades (from cards) with only "Toronto" written and the Kings' word and crown in the logo become just an "LA" with a slightly different shape.

Continuity: The scene in the water after our two heroes have been fighting in the boat and Sheriff Dep. boat comes upon them: Notice Riggs's forehead hair - up, down, up, down... and both their hands keeps changing grip on the boat.

Continuity: During the chase, an articulated lorry skids. If you look during one of the shots you can see that the trailer part is skidding over skid marks that already exist, obviously from previous takes.

Deliberate "mistake": At the end of the film, Riggs shoots Travis through the blade of a bulldozer. While essential to the plot, no pistol caliber of any kind, even "armor piercing/cop killer" bullets, would pierce an inches thick, solid steel bulldozer blade.

Continuity: In the scene where the bad guys have taken the Captain hostage and are in the garage about to steal the guns, there's a closeup between the Captain & one of the bad guys talking. As the Captain turns, you can see an extra at the back wall dressed as a cop. He leans forward a little like he's supposed to jump in, then backs off. He's not there before or after that.

Continuity: When the suspect is shot in the interrogation room, we can clearly see blood on the wall behind him. But when Riggs walks in and sees him, there's no blood visible.

Continuity: As the villains attempt to flee, they and Riggs drive onto a section of freeway that is being newly constructed. However there are already skid marks on the road surface, which is of course impossible, unless lots of people have screeched to a halt right at the edge of the freeway...