The reveal that Lee has an adoptive brother on the wrong side of the law adds a new dimension for why he is such a stickler for the rules. No one would respect such an upstanding officer of the law associating with a Triad member.
In the first movie, Carter rants to Lee: “I’m the president, I’m the emperor, I’m the king. I’m Michael Jackson and you’re Tito.” Aside from the allusion to Chris Tucker and Michael Jackson’s friendship, this line also alludes to the fact that Carter’s name is just a formal version of the name of one of the former U.S. presidents, James “Jimmy” Carter.
When Soo Yung courageously attacks her kidnappers, it could come off as her just defending herself…until you remember a certain throwaway line that Lee mentioned to her earlier about “practicing her kicks and eye gouges”.
In movie one, there’s a brief moment where, while holding Lee at gunpoint, Sang winks at him. It’s never brought up or harkened back to later, so it can come off as a bit strange—that is until you realize that in certain Asian cultures, winking is considered impolite or even offensive.
Carter has an almost sociopathic response to accidentally getting people injured. In the first movie, he causes a shootout that costs an officer his pinky finger and in the third film is mentioned to have shot Isabella in the neck resulting in her and Lee's break-up.
Getting kidnapped twice can't possibly be good for poor Soo-Yung's mental state. Especially since both times were done by a family friend betraying them.
