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: 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: 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.

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...

Continuity: In the underground scene, Riggs runs into the tunnel in trainers and come out wearing boots.

Continuity: When Riggs is following the villains' pickup truck, they make a left turn into a highway and a Delta plane is spotted landing. In the next shot, definitely showing the same turn (note the billboard in the background for "CBS FM" which is in the same place, etc.) the plane changes into an American Airlines plane - note the disappearance of the "Delta" logo and word at the front, and that the Delta plane has a single thin red line, whereas the AA plane has a blue, white, and red stripe along it.

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