Continuity mistake: When Kaylee asks Inara whether or not the Jiangyin Prairie Paradise plate would make a nice gift for Simon, the position of the plate rotates approximately 45 degrees to the right between shots in Kaylee's hands. (00:07:55)
Suggested correction: I just watched this episode, and the camera was off Kaylee long enough to rotate the plate in her hand, especially if she's fidgeting with it in her hands.
Factual error: Jayne doesn't need the suit to fire his gun, because ammunition contains an oxidizer that would allow it to be fired even without oxygen present.
Suggested correction: From a different perspective it's not a factual error. Because Jane shot multiple bullets. It means the gun still can be shot after the space suit case got pierced from the first bullet. So it's a possibility that the characters thought wrong (even though it's a bit silly for space travellers to not know this fact but doesn't mean it won't happen).
