Continuity: When Tracey's coffin is opened aboard Serenity, Jayne takes off his "silly hat" in respect. In the very next shot, he has the hat back on his head. Also, the hat appears in Jayne's hand in the space station before he has even taken it out of the box.
Crew or equipment visible: Towards the end, when Tracey is threatening the crew with a gun into the ship's bridge, just after more snow hits the ship, a crew member's hand can be seen on the left, behind the window, grabbing a piece.
Continuity: The wood shaving's on Jayne's hat constantly change between shots, starting from the very first time he puts it on his head in the space station.
Continuity: The straw on Jayne's knit cap disappears and reappears repeatedly.
Continuity: When all of the crew are around the Coffin, listening to the recording, Jayne removes the hat his mother made. The camera cuts back to the crew and Jayne still has his hat on.