There's a lot of Chinese dialog and signage
, comparable to its usage in the series. Also other Asian cultural influences, like the Companion house and the Japanese-style Fruity Oaty Bar commercial.
And there were definite Western elements too, particularly in the opening heist. It's just that the movie focused mostly on other aspects of the universe, which was never strictly
a "space Western" (see "Ariel" -- the core worlds were much more high-tech and urban). It's possible those aspects were de-emphasized in order to make the movie more accessible to the general audience, but maybe it's just that the story Whedon had to tell focused more on other facets of the 'Verse. After all, while the series took place mostly on the outskirts of civilization, the movie dealt more directly with the Alliance and its agents and activities.