there do be spoilers here
Now that Firefly has been canceled, there are several puzzles that us Firefly fans may never know the answers to. Among these are:
The relationship between Mal and Inara. It is obvious that Inara is in love with Mal. Mal may feel the same way, however we see only one or two glimpses of these underlying feelings during the few aired episoses. It would have been interesting to see how their relationship evolved during the course of the series.
The relationship between Simon and Kaylee. Pretty cut and dry, but we'll never know how it pans out.
The relationship between River and the Alliance. The Alliance experiemented around inside River's head, imbuing her with psychic and extra-sensory abilities. It is possible they were trying to turn her into some sort of asset for their spooks. It is implied that River may possibly be telekinetic, but we never see any evidence of this. Simon manages to perform a neural scan of River in the episode Ariel, however the series ends before we learn the extent of the Alliance's doings. We also do not find out exactly who are the men in black following her, or why they kill everyone that crosses paths with her.
The relationship between Book and Inara. It is very possible that Book and Inara crossed paths before meeting again on Serenity. They show a casual familiarity in the pilot episode that goes beyond new acquaintances. It is strongly implied that Book's first occupation was not a preacher, and has his own trouble he's running from. He has, or at some time has had, some importance in/to the Alliance, as in one episode he produces an unknown ID Card to Alliance soldiers, who immediately whisk him off to their hospital. He is also intimately knowledgeable in firearms, and is quite capable with them. I personally believe that Book was an Alliance soldier ...
There are many chinese phrases spoken between the characters, chinese imagery and writing in many of the cityscapes we see. I'm not sure if this serves to demonstrate blending of cultures from the old earth, if there is some deeper meaning, or if the writers just really liked the stuff and included it.