Trivia: The B.F.G. is a weapon that dates back to the game "Doom" back in 1993. There, it was the 'ultimate' weapon which, when fired, cleared the screen of foes in a great sickly green blast, consuming enormous amounts of ammo. It has showed up in various later games by both ID Software and third parties. Up to this movie, the acronym was never explained directly - although Sarge's version, "Big f**king gun" was for a long time the community's accepted name (also used in the original Doom design document, but not the game itself), and is most likely a homage to that.
Trivia: At one point Sarge tells his men to kill the remaining civilians to prevent the infection from spreading, an order which they all refuse. According to the back story of the first Doom game the reason the main character was sent to Mars in the first place was because he refused an order to kill innocent civilians.