Jaynestown - S1-E4
Visible crew/equipment: When Simon poses as a buyer and gets a muddy hand print on the back of his suit, he and the gang are given a tour of the mud complex. In the first shot, the shadow of a camera can be seen on the ground in the very bottom left corner of the screen.
Jaynestown - S1-E4
Continuity mistake: Right after Simon gives his "box dropping man ape gone wrong" line, as Kaylee says "you're pretty funny", he starts to take a drink. When Kaylee finishes talking, the shot changes to in front of them both and Simon's hand and mug are now in his lap.
Jaynestown - S1-E4
Continuity mistake: The mud left on Simon's shoulder by the foreman slapping his back disappears soon after, despite him having had no opportunity to change or clean his jacket.
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 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: 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.
Continuity mistake: During the duel, after Atherton breaks Mal's sword, he puts the blade to Mal's chest with his arm straight and his wrist slightly bent. The angle changes, and Atherton is suddenly holding the sword with his elbow bent and a straight wrist, in a completely different manner. (00:37:30)
Continuity mistake: At the beginning of the episode, Mal, Jayne and the slavers are playing holographic snooker. One of the slavers gets ready to hit the white ball and leans over the table with his snooker cue. The holographic balls then start to malfunction. In the shot of them malfunctioning the snooker cue that the slaver was holding has disappeared from the table only to return in the following shot.
Visible crew/equipment: Right after Kaylee tells Mal that she's not speaking to him there is a wideshot of the ballroom dancers. In the archway at the back of the room Joss Whedon, the director/creator, walks into shot wearing a Hawaiian shirt, shorts and a baseball cap with headphones around his neck. Just as he raises his hands to speak to the dancers the shot cuts to Inara and Atherton.
Continuity mistake: After River brings Simon the hodgeberries, the hair on her left shoulder constantly moves between shots.
Continuity mistake: In the opening scene where Simon is talking to his father about his dedicated source box, a newspaper on the table in front of his father keeps moving between shots.
Continuity mistake: As the crew leave Simon and River behind on Jiangyin, Simon's fringe changes between shots. In some there are 3 curled strands of hair, in others there are 2.
Continuity mistake: When Serenity disembarks from the Alliance ship after getting Shepherd Book stitched up, the lights on the port (left) and starboard (right) sides of the ship are reversed - the port lights are green when they should be red and the starboard lights are red when they should be green.
Revealing mistake: In the scene where Simon's dad bails him out of prison, there is one shot showing a very long corridor. It is only seen in this one shot, doesn't appear to have any depth to it and there are no people walking in it. That's pretty unlikely for an Alliance prison. I'm thinking that it is a backdrop.
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.