Visible crew/equipment: Tracey threatens the crew with a gun on the bridge when he hears that they're about to call the cops. He says that he'll blow a hole right through Wash if they do. There is a shot of Mal saying "You mailed your ugly business to Zoë and me, Tracey." As he says this, a crew member's hand can be seen above them (through Serenity's windshield on the left of the screen) grabbing one of the pieces of fallen ice.
Visible crew/equipment: When the fake ambulance that the crew made to infiltrate St. Mary's hospital lands at the main entrance, it lands on flat foot pads. But in the following shots the casters that were used to move the prop around the set are visible beneath the landing feet.
Visible crew/equipment: As the camera goes down through the ship to River standing on the catwalks in the cargo bay (eavesdropping on the crew as Kaylee tells them about how she killed the 3 guards on Niska's ship in War Stories), look at the kitchen table on the far right of the screen. There is a man with white hair bent over the table reading a book. He isn't part of the ship's crew, more likely part of the film crew.
Visible crew/equipment: Right after Kaylee tells Mal that she's not speaking to him there is a wideshot of the ballroom dancers. In the archway at the back of the room Joss Whedon, the director/creator, walks into shot wearing a Hawaiian shirt, shorts and a baseball cap with headphones around his neck. Just as he raises his hands to speak to the dancers the shot cuts to Inara and Atherton.