First of all I, like many other posters, am really glad we got to watch this movie because it became clear to me how pervasive its influence has been. From the plot of Mortal Kombat (which is said to have been based on this film) to the villain in the cartoon series Inspector Gadget (an iron-clawed figure always shown stroking a white cat, much like the villain in Enter the Dragon) to the omnipresent shrieking noise (which--I agree with others who have said this--really did cheapen many of the action scenes), this film really seems to have left its mark on popular culture in ways that I was previously unaware of.
As to the film's portrayals of Asian people, I thought it was interesting that both the main bad guy and the main good guy were Asian, rendering Lee's defeat of the main villain free from racial power dynamics. Although we do see Bruce Lee kick some white people's butts (most notably that of Oharra), none of them are truly worthy opponents (Oharra fights unfairly and his death is seen as justifiable anyway because he is responsible for the death of Bruce Lee's character's sister). I can't help but feel that this is not just a coincidence. Would it have been taboo to have depicted Lee triumphing over a white opponent who was actually a real match for him? I for one would have been excited to see such a blatant overturning of racial power dynamics. Unfortunately Enter the Dragon chose not to "rock the boat," opting to take the safe route of pitting Lee against an Asian villain.
Moreover, Lee (as many others have noted) was desexualized in his portrayal. Although I was glad that, unlike the other men, he would not pick a woman from the harem to be his sex slave (soo sexist!), it did set him up as being different and somehow less of a man than Roper and Williams (the other two "good guys"). Even if Lee didn't pick a woman from the harem, I am so used to the heroes of action movies ending up with a beautiful woman that the fact the Lee had no love interest whatsoever seemed strange and reinforced this notion of the Asian man as asexual.
Even so, Bruce Lee's fighting was truly awe-inspiring--so graceful and yet so effective--and I found it gratifying to see such a powerful Asian man in a mainstream American movie. Granted, his fight scenes were made somewhat comic by the ridiculous shrieking noises that seemed to be dubbed in, but Bruce Lee was nonetheless quite a force to be reckoned with, and I have no trouble understanding why he is seen as an icon by many young Asian Americans (particularly boys).
My Chinese American fiance was certainly a fan, although perhaps not Lee's most devoted fan. He admits that he never really liked Lee's American films, feeling that he was always portrayed with more depth of character in the films he made in Hong Kong. He actually has a rather large collection of subtitled Asian movies and has always been more of a fan of the films of Stephen Chow, but I wonder how many other Asian Americans have had that exposure. I suspect that nowadays (owing to globalization, etc.) that number is relatively high, but in the 1970s Bruce Lee may have been one of the few Asian film stars young Asian Americans ever saw. Whether or not this is the case, he was and remains one of only a few Asian actors to make it big in American mainstream cinema, and so I cannot help but feel an affection for Enter the Dragon, even as I reject some of its more problematic elements.