The long Chinese phrase Wash angrily yells at Zoe on the bridge translates (roughly) as "Shove all the planets in the Universe up my ass!".
On the DVD commentary, Alan Tudyk pointed out that despite the way Zoe and Wash were constantly portrayed, with Zoe being taller than her husband, Alan is in fact taller than Gina Torres. He is 6', she is 5'10''.
In the opening scene, where Simon and Book are discussing the operations performed on River, Simon is looking at a computer display of River's brain. The text that scans past underneath the brain model is lines of Javascript code from a web page.
Episode #10 in the "Joss Whedon Intended Timeline" for "Firefly" and NOT as Fox dictated the episodes were to be run.
As Firefly docks with the space station, the guard appears to be reading an advert for "Stop Staring!", a real 20th century company that sells vintage clothing.