Out of Gas - S1-E5
Continuity mistake: In the flashback where Mal and Zoë meet Jayne for the first time, every close-up of Mal and the one close-up of Zoë shows their hair blowing in the wind. But in the shots of them together, their hair is completely still.
Out of Gas - S1-E5
Continuity mistake: One of the candles on Simon's birthday cake keeps blowing out and re-lighting itself between shots.
Out of Gas - S1-E5
Continuity mistake: Kaylee has just put Simon's birthday cake down on the table when the explosion happens, but in many subsequent shots of both the table and the floor in the dining room, the cake is nowhere to be seen.
Out of Gas - S1-E5
Continuity mistake: When we see the flashback of Mal and Zoë first entering Serenity's cargo bay, just after Mal has bought the ship, there is a cable on the floor behind them. For a short moment, we see the cable being dragged over the grille right behind them, then the shot changes and there is nothing there at all; the only cable is much further back and lying at a completely different angle. (00:01:55)
Out of Gas - S1-E5
Continuity mistake: In the first flashback in the episode, Malcolm is showing Zoe Serenity after buying it. You can see on his left arm the stitched-up bullet hole that was from the very first episode when Mal gets shot. This episode would have taken place much later than the flashback.
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.