Continuity mistake: 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 mistake: 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.
Trivia: After the building collapses in the beginning, the bomb-squad guy who claps (making fun of Riggs's and Murtaugh's goof up) is in real life Bill Frederick, the mayor of Orlando at the time the scene was filmed.
Riggs: I can't shoot a dog. People? Okay, but not dogs.