Corrected entry: When discussing the Reavers, Shepherd Book has a cord sticking out between the back of his shirt and the back of his neck. It seems to be an audio cord but could be a part of his pony tail as well. Whatever it is, it's definitely out of place during the shot.
Corrected entry: When the Feds are searching Serenity for River and Simon (who are in spacesuits on the outside of the ship) one soldier picks up and flips over the placemats on the table. This is pointless because, obviously, there's nothing that could have been hiding under them.
Corrected entry: When Simon enters the derelict ship wearing a space suit and sees everyone else without suits, he puts his flashlight down and starts struggling with his helmet. The viewpoint changes to show Kaylee moving toward him - with his flashlight beam waving over her face and body. Then we cut back to Simon, who is still struggling with the helmet with both hands - he's not holding the flashlight at all.