When you first see a Jackie Chan film, you can't help but notice that something is missing: Hero (Chan) approaches edge of building, looks back at crooks, and then jumps, with camera following him the whole way down. He gets up and doesn't have time to brush off his clothes because more bad guys are waiting for him at the bottom. There are no edits and no stuntman to replace the big star.
Chan does it all, and the rough-around-the-edges production style of his Hong Kong produced films add to his dynamic screen presence. But Rush Hour is Chan's first big budget American film, and safety conscious Hollywood requires him to take fewer risks while still trying to show off his talents. Consequently this movie pulls out pistols, bombs, and a comedic partner to fill the gaps between Chan's stunts.
Many people are shot in this film, along with a multitude of others who are kicked, punched, and hammered on with various martial arts moves. Another red flag for parents is Chan's co-star, comedian Chris Tucker. A PG-13 version of Eddie Murphy, he has a cocky attitude and spews forth a litany of moderately offensive profanities.
That aside, I have a soft spot for Chan. His stunts are usually done as a last ditch effort to get him out of a jam and he often shows compassion toward his opponents. He's not an invincible superhero, but instead reacts to what's happening around him. When he gets hit, he shows pain. These elements make him a more complex character, and this opens the magic gate to the audience: We care about him.
If your older teens are interested in his work, look for some of his other PG-13 titles. Another recent release, Who Am I?, offers more Chan and less blood than Rush Hour. Still, preview any Chan movie first to see if it meets your family standards. Also, take time to explain to your teens that Chan is trained to do those amazing stunts. Don't try this at home kids.