If Season 2 had been directly following Season 1. we could see how and why Inara and Book decided to leave "Serenity." Also, I would have liked to have some episodes going back to directly after the war, maybe find out when and why Mal and Zoe decided to buy a ship together, learn some of Book's past history, and I think that there would be a great potential for comedy if Jayne's mother showed up for a visit (Jayne would have, of course, told her that it was HIS ship, all the others worked for him, and Inara was his personal Companion.
A post "Serenity" Season 2 would have to introduce at least one or two new characters in order to replace Wash and Book. I think that having the Nameless Operative join the crew as the new pilot/flight engineer would be a good twist, and River might adopt Mr Universe's love bot (Jayne smuggled it on board, but it refused to cooperate with him because it's programmed to only love Mr Universe) Of course, the love bot might not work, since it might be compared to Data or some other sci-fi robot character. However it happens, I think that, since River is apparently recovered from her brainwashing after "Serenity," having a close friend, or maybe even a lover, would be appropriate.