LOL. I just knew someone would call me on this.
Want to hear something funny? I'm Chinese and I already know this. My two daughters call each other Mei-Mei and Jie-Jei. It's just that Simon's tender expression makes it feel like a term of endearment. In my interpretation of the Firefly universe folks would use the Chinese word as a term of endearment. It certainly seems that way because, in other settings, he calls her his "sister." I know it's my personal interpretation but it's a plausible one and makes the scene much more effective for me.
The actor who seems to have the hardest time acting through mock-Chinese is Ron Glass (Book) - but I only recall one scene where he speaks it. Everyone else seems to do a stellar job ... especially Mal, Kaylee, Inara and Simon ... if only because the Chinese phrases don't impair their credibility at all.
The mangled Chinese and absence of Chinese main characters don't bother me at all, even though it probably should. Most of the time I have no idea what they're even trying to say. I can make a million excuses for it (e.g. perhaps bad Chinese is thrown around like Spanglish is tossed about today), but it still works for me when the actors strike a rhythm in the unintelligible dialogue that can still relay meaning (not unlike R2D2's noises). For example in "Ariel" when Mal is trying to learn how to speak like an EMT from Simon he exclaims, in frustration, "Dialated! Dialated! Ching-wao tsao duh liou mahng! ... Shiny." (I cut and pasted the "Chinese" because I still don't know what he was saying ... but it's still funny.)
Similarly I have no problem with the absence of Chinese main characters. Not every ship crew will be a proportional representation of the population. For all we know maybe the Chinese population is concentrated more on specific worlds, or maybe smuggling/piracy/space travel isn't a vocation that many Asians gravitate towards. I prefer to believe that different ships have different ethnic mixtures. I don't need to have a token asian aboard the Firefly.