If I'm not mistaken, Gina Torres is Cuban American, not African American. So, there is one African American, one Cuban American, and 7 white crew members. But yes, more Asian characters would make sense even if they were not crew but characters met in the 'verse.

The cast was perfect.
WHAT is it with you people all whining about not enough characters that are non-white?
Sorry but it would have sucked changing the characters.
They who give up liberty to
obtain a temporary safety deserve
neither liberty or safety

If I had to change anything I'd have Shepard and Zoe both be Chinese and maybe change one other character to be Chinese. Basically space would be America and China and the likelihood of a lot of black people being chosen for the escape from Earth is pretty small. Go ahead and call me racist if you want but it'd probably be like 90% white based on who was investing and working on the space programs for NASA. The chance for two of the nine crew members to be black would be much smaller than for them to be Asian.

Taken from the Trivia section:
The Alliance's full title is the "Anglo-Sino Alliance." Joss Whedon intended for it to be the merger of USA and China, the last of the world's superpowers. That's why many characters sometimes speak Chinese. The Alliance flag, seen in the original pilot, is a blending of the US and Chinese flags.

A random language that was easy-ish to speak for all actors on the odd one off?
One of the harder languages I learnt was Latvian, there's not many people who teach it and while it was close to Russian I sounded like a right twat speaking it.

Yeah. I remember some people mentioning that when the show first aired. I myself find that the one true flaw of the show. No Chinese in the main cast. Heck, very few Chinese at all.
Seize the moment, 'cause tomorrow you might be dead.