Continuity mistake: In the final shot of Serenity leaving Regina near the end, 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.
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.
Revealing mistake: In the scene where Mal and Zoë exit the train, look closely at the woman in the yellow veil to the left of the screen holding a baby - she walks into a passing vehicle knocking her baby on its head (revealing it is really a doll).
Continuity mistake: When Mal is fighting Crow on the ship, he falls over the containers of medical supplies, knocking some of them over. A few shots later when Jayne shoots Crow, the containers are standing upright again.
Bushwhacked - S1-E2
Revealing mistake: As Mal rolls the survivor of the derelict transport onto the floor, the survivor moves his left hand onto his chest when he is supposed to be unconscious.
Bushwhacked - S1-E2
Audio problem: When Zoë and Mal find the door to the cargo hold, Zoë checks to see if it's locked. Four beeping sounds can be heard as she does this, but she doesn't press any buttons. She only turns a knob on the door. The four beeping sounds are also heard before she even touches anything.
Bushwhacked - S1-E2
Continuity mistake: When Kaylee and Simon go looking for spare parts on board the derelict ship, there are two green lights lit up on a control box behind Kaylee. But once Kaylee pulls one of the ship's parts out, the two green lights are no longer lit. Several lights in the room flicker and flash on/off, but the two green lights on the control box behind Kaylee do not.
Bushwhacked - S1-E2
Continuity mistake: After Simon and River come down from Serenity's roof, River asks Simon if Mal is coming back. Simon tells her that he is. River's head then moves from looking down to looking up between shots.
Bushwhacked - S1-E2
Visible crew/equipment: As Simon boards the derelict ship, a handheld camera is reflected in his visor.
Bushwhacked - S1-E2
Visible crew/equipment: As Zoë and Mal investigate the derelict ship, stage lights are constantly reflected in both their visors.
Bushwhacked - S1-E2
Continuity mistake: As Mal tells Commander Harken that the Reavers made the survivor watch as they killed everyone on board, Commander Harken's hands move from separated to clasped together on the table.
Bushwhacked - S1-E2
Continuity mistake: At the beginning of the episode, when Inara asks Simon how River is, River's hair is hanging down behind her back on both sides. But when Simon tells Inara that she still won't talk about what was done to her at the Academy, her hair is hanging in front of her right shoulder. A few shots later her hair is hanging behind her back again.
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)
Continuity mistake: When Inara finds Mal unconscious in his quarters, his head is resting up against the wall. When the angle changes to show her running over to him, he has moved away from the wall and his head is on the floor. After she has called for help, his head is once again up against the wall. (00:31:00)
Continuity mistake: When Shepherd Book tells everyone about the electrical nets, Jayne says, "One day you're gonna tell us all how a preacher knows so damn much about crime." Shepherd then turns to leave. But in the immediate close up of him and Mal, he turns to leave again.
Continuity mistake: When Zoë and Wash are on the bridge talking about Saffron, Zoë's necklace moves position between shots.
Continuity mistake: Just before Serenity disembarks from Triumph near the beginning of the episode, there are some small areas of shrubbery and foliage surrounding the exit ramp. But once Serenity takes off, the shrubbery and foliage is gone.
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).
Visible crew/equipment: In the celebration at the beginning, the shot where Jayne receives the rain stick, a camera crew is briefly visible just to the right of Jayne's head right before he says "I will treasure this."
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)