Bruce Lee actually struck Jackie Chan in the face with one of his fighting sticks. He immediately apologized and insisted that Chan could work on all of his movies after that. Unfortunately, Lee died before he could keep his promise.
Bruce Lee suffered some on-set injuries. His hand was severely cut while shooting O'Hara's death scene, when Bob Wall mistimed his thrust of the broken bottle towards Lee (fake glass was not available). When Lee held the poisonous snake that guarded the secret entrance to Han's drug lab, the snake bit Lee. Fortunately, the snake's venom gland had been removed.
Warner Brothers wanted to call the film 'Han's Island' because they thought international audiences would be confused by an action film titled 'Enter the Dragon'. Other alternate titles were "Blood and Steel" and "The Deadly Three", a reference to 'Bruce Lee', John Saxon, and Jim Kelly's characters.
After Bruce Lee cut his hand on the bottles (a miscue by Bob Wall), he hit Wall with a "real" flying kick in a subsequent scene. Even though Wall knew it was coming, he was knocked into the man behind him so hard both of his arms were broken.
The trivia items below may give away important plot points.
Kien Shih did not speak English, and mouthed his lines as best he could. Chinese-American actor Keye Luke overdubbed his dialogue. Luke also narrated an earlier scene depicting the death of Bruce Lee's sister.
Originally, Han was going to kill Roper, and Williams and Lee would fight Han's army at the end. Roper's and Williams' roles were reversed by John Saxon's agent.