There's not a lot of detail out there, but Joss Whedon has made a few comments about Firefly season two. In particular, in August 2010, he told SciFi Australia:
Joss answered this point blank with "Serenity pretty much covered it" (Firefly Season 2). "Finding the truth about Miranda, the origins of River, that was all going to be told over Season Two."
The Wikipedia article for the movie cites the Serenity Collector's Edition DVD cast commentary when it says:
"He based his story on original story ideas for Firefly's unfilmed second season. Whedon's original script was 190 pages, and attempted to address all major plot points introduced in the series. After presenting the script to Universal under the title "The Kitchen Sink", Whedon was asked to cut down the script to a size filmable under his budget constraints."
(Note that a good rule of thumb is a minute of movie for every script page. So that's a three-hour-plus Serenity.)
There are other unanswered questions: Book's background (covered somewhat in some of the comics), and Inara's illness and syringe (confirmed by Morena Baccarin) for instance. They might have been revealed somewhat in the second season, perhaps, or maybe later. Who knows. There's a good chance that Joss accelerated some of his plans that could have been spaced out over a decade or two (okay, that's a little too extreme). And we'll obviously never know what might have happened to appease/anger the shippers.