Trivia: One of the first scenes to be filmed was where Jackie jumps from the base of the bridge to the hovercraft. Unfortunately, he broke his ankle doing it and ended up in plaster. A sock that looked like a trainer was created to go over the plaster and Jackie filmed the rest of the movie with a broken ankle. If you watch through the titles, you can see him showing off the sock.
Trivia: It was actually filmed in Vancouver (due to production concerns). At first they tried to hide this fact by using camera angles that hid the mountains and having graffiti painted (and removed at the end of each day). In the end they decided to just film the action and not worry about hiding the location: people should be watching the action, not the background...
Trivia: "Rumble in the Bronx" is oft-considered Jackie Chan's first major breakthrough hit in the US. The film was among the first of Chan's films to receive a wide American release, in addition to general critical and commercial acclaim.