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.
Firefly (2002)
1 visible crew/equipment mistake in Objects in Space
Starring: Alan Tudyk, Nathan Fillion, Adam Baldwin, Morena Baccarin, Gina Torres, Summer Glau, Jewel Staite
Jaynestown - S1-E4
Visible crew/equipment: When Simon poses as a buyer and gets a muddy hand print on the back of his suit, he and the gang are given a tour of the mud complex. In the first shot, the shadow of a camera can be seen on the ground in the very bottom left corner of the screen.
Mal: Now, you can luxuriate in a nice jail cell... But if your hand touches metal, I swear by my pretty floral bonnet I will end you.
Out of Gas - S1-E5
Trivia: Wash sets up a big red button for Mal to push to call back the shuttles if help arrives. He tells him "When your miracle gets here, just hit this button". After the show got cancelled, Alan Tudyk sent the button to Joss Whedon with the same message enclosed.
Question: In some scenes, why do the Serenity crew members speak Chinese?
Chosen answer: One of the premises of the show is that the two major Earth societies that survived, and ultimately merged, were the Chinese and Americans. As a result the common language includes much Chinese. Clothing, signage, and building designs also have a heavy Chinese influence.