The Message - S1-E15
Continuity mistake: At the beginning of the episode, when Jayne reads in the note from his mother that she enclosed something in the box for him, there is a shot of Zoë reaching for a crowbar to open Tracey's coffin. Jayne's left hand is visible on the far right of this shot, holding the hat that his mother knitted for him. In the following shot he takes the hat out of the box despite already having it in his left hand in the previous shot.
Continuity mistake: After the opening credits River wakes up from a nightmare. She knocks over a rolling tray and some objects fall off it onto the floor. The position of the tray and the objects left on it changes between shots.
War Stories - S1-E9
Continuity mistake: In Niska's office, behind his desk, there is a door that slides open to a small torture chamber. In "War Stories," there is a small staircase that leads into this torture chamber behind the door. However, in "The Train Job" (the first time we see this chamber) there is no staircase.
Continuity mistake: At the beginning of the episode when Mal, Jayne and Zoë are ransacking the destroyed ship for supplies, after Mal says "Vault's sealed" there is a shot of Mal as he inspects the door hatch before asking Jayne for the explosive gel gun. The ring around the door hatch's handle from the explosive gel gun is already visible in this shot.
Continuity mistake: The first shot we see of Nandi waking up shows her hair loose on the pillow, and her hand curled up on the sheet beside her; in the next shot, a close-up, her hair is mostly tucked behind her ear and her hand is closer to her face than previously. (00:25:10)
Continuity mistake: When Saffron first hits Wash, he falls with his head in the centre of the doorway (from our point of view), but a second later, when she goes to lift his legs through the door so she can shut it, his head is noticeably more to the left (again, from the viewer's point of view). (00:27:05)
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.
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: When the foreman first slaps Simon on the back, the muddy handprint has quite identifiable finger marks, but in the next shot, when Simon is walking away, the muddy shape has changed. In a subsequent shot, the mudprint has disappeared entirely. (00:04:25 - 00:06:00)
Continuity mistake: When talking to Saffron after being caught by her husband while holding the Lassiter, Mal refers to her as 'Yo/Saff/Bridge', an amalgam of her three aliases, Yolanda, Saffron, and Bridget. The subtitle reads this as "Speaking Chinese."
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.
Continuity mistake: When Nandi is killed, she falls to the floor on her back, her left arm by her side and her right on the floor by her head. We see her in this position a number of times, but when Mal and Inara look at one another at the end of this scene, Nandi's left arm is now lying across her chest. Neither of the other characters did this to her. (00:35:00)
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.
Continuity mistake: After Durran calls the police and Mal and Saffron try to escape, they leave the Bellerophon Estates through a door which uses a crash bar to exit. However, when the guards arrive at the door, it has changed colour and has suddenly started using a regular handle.
War Stories - S1-E9
Continuity mistake: In the scene where Malcolm Reynolds is being tortured, after Zoë takes Wash away, the villain cuts off Malcolm's left ear. The shot changes, and then returns to Malcolm, showing the other side of his face. Now the visible ear, the right one, is missing. The shot changes to the front, and now his left ear is missing 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.
Continuity mistake: In the close-up shot of the explosive in the sticky substance being applied to the outside of the cargo hold, the pink wire sticks out at the bottom, and in a loop in the middle. In the next shot, from slightly further back, the wire doesn't stick out anywhere, and the shape of the explosive ring has changed and become more oval. (00:05:30)
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.
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.
War Stories - S1-E9
Continuity mistake: The size of the red marks on Wash's body change from when he first leaves the torture chamber to going into the cockpit of the shuttle.
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.