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.
Trivia: The Alliance troop uniforms are the exact same ones used in Starship Troopers (mentioned on the commentary).
Trivia: When the crew returns from their raid of the Alliance hospital, Malcolm grabs Kaylee from behind and holds her in a friendly hug. This was improvised by Nathan Fillion, and was left in the shot because Joss Whedon felt it was such a natural movement for Malcolm to make. (00:37:00)
Trivia: As Mal is bringing the shuttle in to land at the floating luxury home, as he flies to the left of a tower towards the gardens, behind them flying from right to left is the unmistakable silhouette of an SR-71 Blackbird cruising by. Given that this is a planet for the super rich and the heist is of a well known collector of old Earth artifacts, maybe this plane is part of another collector's collection, like John Travolta and his small fleet of planes including an airliner and other exotic aircraft.
Trivia: Just an interesting thing to note. The villain of the episode is an unhinged character named "Jubal Early," and is played by Richard Brooks. Six years earlier in 1996, Brooks starred in the film "The Crow: City of Angels," where he also appeared as a similarly unhinged villain... with the remarkably similar name "Judah Earl." Just a fun, odd coincidence.
Trivia: According to Joss Whedon and Nathan Fillion in the DVD audio commentary, Whedon had originally written the role of Badger for himself.
The Message - S1-E15
Trivia: The funeral music heard at the end of "The Message" was written by the show's composer right after the series got cancelled. The theme was actually inspired by his sadness that the show was ending.
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.