The ignorance of Chinese culture is obvious from all the things Firefly simply got wrong. I don't really have a problem with the cast's dreadful pronunciation; it's not fair to blame English-speaking actors with no previous training in Chinese for that. It's all the other stuff: phrases that that are dictionary-correct, but not anything a Chinese person would actually say, phrases that are just plain wrong. Chinese characters written back-to-front, written in the wrong order, lying on their side, or muddled up with Japanese. Occasionally there are gibberish pseudo-characters that don't mean anything as far as I can tell. In at least one episode, a recorded "Mandarin" announcement is actually Cantonese (correctly pronounced for once) because they gave a written script to somebody, and apparently forgot to tell him which dialect to read it in. Trying to explain away these blunders as "cultural change" raises the awkward question of why the English language has not been butchered to the same extent by the "fusion". You'll have to take my word for it that the Chinese in Firefly is many times more "variant" from today's usage than the English.
My accusation that Firefly exhibits a neo-colonialist attitude requires a bit more explanation. Colonialists essentially regarded everything about the peoples and territories they conquered as theirs for the taking. They felt entitled to ascribe or deny worth, on the basis of their values and judgements, to every part of native cultures, and to separate, physically and socially, cultural artefacts from the people who produced them. They would happily collect Tang Dynasty bronzes, for example, as superb works of art, while refusing to admit Chinese people to their homes, except perhaps as servants. The cultural appropriation was all too literal in those days.
The balance of power in the world has changed, and colonialists can't march about in pith helmets looting Chinese palaces any more. However the underlying attitude of, for example, modern Western museum curators to their often ill-gotten collections is essentially the same as their ancestors': "We stole this stuff fair and square, and we're keeping it." They also share the same attitude that it is acceptable to separate the products of a culture from the culture that produced them, not just physically, but conceptually as well. To declare, in effect, that a culture's "stuff" is cool because they say so, but the people who produced it are not and don't have a say in the matter. All that has changed is their ability to exert "hard power" over their erstwhile victims, not the exploitive underlying attitude of cultural superiority, so domination is exerted by "soft power" instead. This is neo-colonialism in my opinion, and the cultural appropriation less literal, but still real.
I call Firefly's attitude to Chinese language and culture neo-colonialist, because it too is essentially the same as that of the 19th century European collectors I mentioned above; that Chinese "stuff" is cool, but Chinese people are not, and that it's perfectly acceptable to separate them. That Chinese people might produce good set dressing, but nobody wants interact with them, or hear their voices. That cultural appropriation is still OK. That treating my native language like Farscape's invented slang is OK.
Firefly simply does not really show any cultural fusion at all. It is just a show about Americans taking place in front of a crudely-painted "exotic" background. The creators never did anything interesting with the "Chinese fusion", or brought it into focus in any story that I can think of, which is why I have previously described their cultural appropriation as not only ignorant and neo-colonialist, but pointless too.
I don't just think Firefly's questionable casting and world-building were bad for what might be regarded as "external" ideological reasons; I think they were bad for the show too. I'm often told that Joss Whedon intended to make Kaylee "Asian", but that Jewel Staite nailed the audition, so he cast her. I'm not sure why that is supposed to make a difference, or mitigate the overall casting problem, and I certainly don't have a problem with Ms. Staite's excellent performance in the role, but I would ask Whedon: "Why choose Kaylee as the Asian character in the first place? How does that strengthen the world-building and story-telling? Did you roll dice for it or something? Is being Asian just a prop or costume for you, like Jayne's hat?"
Suppose Whedon had chosen to cast East Asian actors as the Tam siblings, the only members of the core cast with an arguably Chinese surname, and fugitives from the Core Worlds. This would have opened the door to exploring themes like: the possibility that Chinese-descended settlers had much higher social status on the core worlds than on the frontier (where Wheedon depicts them basically as coolies, much as they were in the historical American West. Ooops!), and what that racial stratification might mean, especially to Simon-the-scholarly-doctor; or that the recent war was a clash between a collectivist, Confucian model of society and an more individualistic American one, mirrored in the conflict between Simon's filial duty to his society, and his personal protective feelings to his sister. Of course these might not be stories that Whedon wanted to tell, and that's fine, but casting and story would have locked together better than making some random character Asian in isolation from the story. Not that I'll ever begrudge an Asian actor a pay-cheque in any role; it's not as if they have many to choose from.
warrants forum threads about how the show was cool and wonderful, then its worth postings from me about how it wasn't.