As I've mentioned before, I take a lot of inspiration from the Gaunt's Ghosts series of books. Part of the fun of the books is that it basically deals with the everyday drama of military life in the Imperial Guard.
So, basically, I took a lot of inspiration from that. I thought about how the various crew members and crew factions were interacting, and how each would respond to their mission differently. Then, I let the PCs deal with the ensuing drama.
One major thing I stole from the Ghosts series is the section of the ship I call "The Follies". The Follies are basically the underbelly of the ship. A place where civilians, hangers-on, and unlisted members of the ship live. It's a tiny little meta-community which allows the rest of the ship to actually function. If you're looking for a red-light district, its in the Follies. Get pregnant while on board and need child care? In the Follies. Looking to gamble? Swap holo-vids? Get black market items? Or even just buy a drink? In the Follies. The Ghosts series refers to that section of a ship the swelter decks or low decks.
Basically, it's where the crewmen go to unwind or just "be themselves" when not on duty. In any case, I liked this idea so much I incorporated it into my game. But I also like it because it's very much a 40k sort of thing to have in a setting. It reinforces the idea of massive ships that sail through the stars for years, and being entire communities unto themselves.
It's a great place for adventure. A Rogue Trader ship could even have its own little underhive! It also allows a Game Master and players to have some "traditional" roleplay. For example, you could stage an encounter at a tavern in the swelter decks or start out a scene with a minstrel playing for an audience. It helps ground the party into something familiar before you go out and do something totally alien and unique.