Continuity mistake: When Early drops an unconscious Mal down the hatch to his room, in the shot from above Mal falls with his arms by his side, but in the next shot when he lands, his arms are above his head and fall to his sides when he hits the ground.
Visible crew/equipment: As the camera goes down through the ship to River standing on the catwalks in the cargo bay (eavesdropping on the crew as Kaylee tells them about how she killed the 3 guards on Niska's ship in War Stories), look at the kitchen table on the far right of the screen. There is a man with white hair bent over the table reading a book. He isn't part of the ship's crew, more likely part of the film crew.
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.