Continuity mistake: In the scene where Jayne is telling Simon and River to keep clear of Saffron, he is holding some things wrapped in tin foil (possibly food). He places them on a table next to him. River then calls Saffron a liar. In the following shot of Jayne, one of the food packets has been torn open. River later says that "Jayne" is a girl's name. The food packet that was torn open is now intact.
Continuity mistake: When the crew are planning how to break into the Bellerophon Estates, Mal and Saffron use Serenity's port (left) shuttle to get to the island. But when Wash flies Serenity underneath the disposal bin, the shuttle is back even though Mal and Saffron have yet to return. We never see or hear of the shuttles being able to return to Serenity by themselves and it wasn't part of the agreed plan.
Continuity mistake: When talking to Saffron after being caught by her husband while holding the Lassiter, Mal refers to her as 'Yo/Saff/Bridge', an amalgam of her three aliases, Yolanda, Saffron, and Bridget. The subtitle reads this as "Speaking Chinese."
Continuity mistake: After Durran calls the police and Mal and Saffron try to escape, they leave the Bellerophon Estates through a door which uses a crash bar to exit. However, when the guards arrive at the door, it has changed colour and has suddenly started using a regular handle.
Continuity mistake: At the end, when Inara is closing the lid on the trash container there are three shots. From behind Inara, she has her gun in her lap (in her right hand) and is waving with her left, but from Saffron's point of view Inara has both hands in her lap, then Inara is back to waving again.
Chosen answer: One of the premises of the show is that the two major Earth societies that survived, and ultimately merged, were the Chinese and Americans. As a result the common language includes much Chinese. Clothing, signage, and building designs also have a heavy Chinese influence.