The fact that the Mandarin/Cantonese the actors were allegedly speaking was horribly pronounced is admitted to on the commentary tracks of the DVDs. It's shoddy work, to be sure, but it definitely slips by me, in the same way that the gibberish the American Indians in Dances With Wolves slips by me. They should have had a dialogue couch, but I can understand how this concept wouldn't receive much attention under the arduous schedule of weekly television.
What doesn't slip by is the complete lack of Asian faces on the series, especially considering the premise, and especially considering the population distribution between the United States and China, the two surviving superpowers (or, the two surviving powers, anyway) after Earth's abandonment. Actually, the history is a bit muddled, since we don't have much to go on beyond a few comments and that montage that opens Serenity, but that seems to be the general idea.