Continuity mistake: When the cast are at the Miranda colony and discover that everyone is dead, there is a rotating shot of River as she realises what happened. Prior to this there is a brief closeup shot of the rest of the cast as they turn to face her. Jayne turns to his right, but in the following rotating shot of River he has turned from his left.
Continuity mistake: While Zoe determines the location of Miranda, there are two shots of Jayne with his arms down by his sides - one where he is standing behind Inara and one with Wash in the foreground. When it cuts back to the shot of him standing behind Inara, his left hand is on his belt. His hand then returns to its original place when it cuts back to Wash.
Continuity mistake: When the crew are in the cockpit talking about Miranda, Jayne is in the background holding his head with his left hand. 5-6 shots later he is holding it with his right hand. On the cast commentary of the DVD, Adam Baldwin says that he did this on purpose "just to mess with continuity".
Trivia: The "one-shot" sequence in the beginning of the film that introduces the crew of the Serenity and the interior of the ship was actually two shots cleverly spliced together, for both practicality purposes (as one mistake could ruin the entire 4-minute scene) and also because there wasn't enough studio-space to build the entire interior of the Serenity as one unbroken set. Eagle-eyed viewers may be able to notice the moment of the splice, right after Mal runs into Simon and they start to descend the stairs. The splice takes place when the camera does a small whip pan from right-to-left.
Trivia: The child actress who portrays the young River in dream sequences had her voice dubbed over by Summer Glau, who portrays the "older" River. This was done so that audiences could more easily realize the child is River. (And thankfully, Glau's voice worked for the child actress). The child actress portraying the younger River was reportedly heartbroken that her voice had been dubbed over.
Wash: I don't know, but if she doesn't give more power to offset the burn through this landing is going to get very interesting.
Mal: Define interesting.
Wash: "Oh God, Oh God we're all going to die"?
Mal: [Talking into the intercom.] This the captain speaking. We might experience some turbulence, then explode.