Well, what I thought was brilliant about it from a conceptual standpoint is that it took space/interplanetary travel and civilization as *literally* a Frontier. Dozens of colonies trying to scratch out a living on worlds that are just your basic, terraformed planet, and the infrastructure and civilization being built literally from scratch. The people inhabiting these worlds are just like you and I: working to make a living, doing their best to get by and provide for themselves and their families. There was a lot of dirt and a lot of seedy types, and the same desperation in some that you find in every day life on earth.
I think it was a very unique approach as opposed to most Sci-Fi where any planet you come across tends to be super-civilized, with gigantic skyscrapers, lush, green fields and every person clean, shiny and amicable. Those archetypes are old and boring, and bear very little resemblance to the reality we live in. I expect that's one of the many reasons why the latest incarnation of Star Trek failed so completely.
In terms of the characters, I loved that they were all full of flaws and disagreements and their own *history*. They're not the perfect characters of Star Trek, where everyone's fit, firm, toned and nearly always smiling and agreeable. The characters on Firefly have rough edges, haunted pasts and unpleasant traumas that lead them to all kinds of interesting scenarios.
In terms of the overall series as such, I like that it, like Buffy and Angel before it, is VERY context-heavy. Not every episode is a stand-alone adventure like in Star Trek, and when something terrible happens to a character in a Joss Whedon series, they aren't just all fine and dandy next week. Events have consequences in Whedon's writing, and characters carry the trauma of the bad things that happen to them. Often, the small events that catch you off guard will also foreshadow greater and more terrible things to come.
In regards, particularly, to Serenity, I love that Whedon is willing to do horrible things to his characters, even kill them off. One of the things I loved about one character's death was that it *Wasn't* some trite, heroic self-sacrifice. His death was out of nowhere, it was meaningless, tragic and uninvited. I, for one, am sick to death of every character who dies in movies and series doing so "for the greater good" or sacrificing themselves "for the sake of their friends/comrades". Life isn't like that, people don't always die in some noble blaze of glory, sometimes they just get blindsided by a chunk of steel through the heart or a stray bullet falling from the sky because some jackass two blocks over has to fire into the air to celebrate the 4th of July. Perhaps one of the best things about Joss Whedon's writing is that he's willing to face these truths and force the audience to face them, too.
Jason