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.
Revealing mistake: When the camera follows a man through a curtain to reveal the Eavesdown Docks on Persephone, an extra in a white shirt, black vest and straw hat can be seen standing still on the left looking straight into the camera. He then looks away and starts walking. He was waiting for his cue from the director. Several seconds later, the same extra is seen again behind Mal and Kaylee walking in the opposite direction he was just going, giving the impression that the scene wasn't filmed on a location but in fact a small set and they could only afford so many extras.