The Message - S1-E15
Continuity mistake: At the beginning of the episode, Jayne receives a hat from his mother in the post, and when he takes it out of the package it is covered in wood shavings or some similar packing material. He puts it on his head like that, but for the remainder of the scene, the hat alternates from being covered in shavings to clean and back again.
The Message - S1-E15
Continuity mistake: The cut the doctor makes on Tracey is small, but once Mal is on top of Tracey, the cut is a lot longer.
The Message - S1-E15
Continuity mistake: In the first scene in which the crew is back on Serenity, they are discussing Mal and Zoe's recent "delivery." Jayne is shown taking his hat off. Two shots later Jayne is shown in the background with the hat still on his head. Six shots later Jayne is shown with his hat in his hand 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.