Rewatching anything you loved years ago is always a risk. There's always the chance that you'll notice flaws you never spotted before, or that it won't live up to your adoring memories. Unfortunately, Firefly turned out to be something of a disappointment.
Is it a good show? Yes. Is it a great show? I'd say so. Is it unique and compelling with some great plotlines and characters? Definitely. But when looked at from an intersectional feminist perspective, it all starts to fall apart.
In short, Joss Whedon is amazing at creating varied, believable and wonderful female characters. But he's not so good at creating stories for them. And he doesn't seem to think through the implications of his work.
These problems are most clear when considering River. Although River touches on many familiar tropes, her background and potential as a character are compelling. She's a child genius, talented at everything from physics to dance, who was kidnapped and tortured by the government in order to be turned into a psychic sleeper agent assassin. She was rescued by her brother and now has to recover from her experiences and the extreme mental instability she now suffers, while everyone else is keen to dismiss her. In theory, it's a wonderful basis for a character. In reality, River ends up sidelined throughout most of the show, always presented through other's eyes, left to mumble nonsense, make the occasional joke, and be rescued or fought over.
Inara presents a similar problem. She is a confident, glamorous and sophisticated woman with a very caring personality, some skill with a sword, and a staunch determination to say her peace and take nonsense from nobody. She presents herself as independent and in control of her life, but she is actually kept under the Alliance's thumb. She is running from something, but what, we do not know. Oh, and she loves the Captain, despite the fact that it would never work. There's so much material to build plots from here! But in episode after episode, she's a side character, used for sensual soft-lens scenes or as a way to bring a male (or, once, female) character into the story for him to step up and save the day. And considering that the writers will proudly talk about their planned storyline for Inara, involving Mal developing respect for her after Reaver gang rape, her plots weren't going to get better any time soon.
Kaylee is the female character who receives the most attention and development, and again, she's a wonderfully three-dimensional character in theory. She's the confident, talented mechanic who also happens to be rather adorable and caring and very, very girly. But again and again, her cuteness is used as a way to punch the viewer in the heart... and eventually, it becomes a bit cheap and predictable. Oh no, Kaylee has been shot! Oh no, a character is holding her hostage and threatening to shoot her! Oh no, someone has broken into Serenity and is threatening to rape her! Her niceness and sweetness makes her the perfect easy target for violence, and although that might be innocuously appealing from a storytelling perspective, it creates a pattern that is lazy writing at best, and makes Kaylee into an object in the story at worst.
On the bright side, Zoe seems pretty perfectly executed as a character. But she's only one of four female crew members, and the result is frustrating to say the least.
Then we come to the racial elements of the show. Firefly is very clear that it's based in a world that has been equally influenced by American and Chinese language and culture. Signs and instructions are in both languages. White characters use "Chinese" slang and swear words, and a lot of the fashions and entertainments they encounter are East Asian-inspired. But, as many people have commented before, there are no Chinese people. A few episodes have stereotypical-looking Chinese actors in the background, especially in crowd scenes. Only one episode has a Chinese (or at least East Asian) actress with a speaking part... Heart of Gold, where she plays a prostitute, and not even one of the two main ones in the story. The show is happy to use badly pronounced Chinese to get around the censors and add an element of futuristic-ness and "diversity," but no members of the crew are part of this heritage. No recurring character is Chinese. No character-of-the-week is Chinese. None of Inara's clients, no speaking-a-few-lines characters of authority, no one they take a job from or fight against. Just one woman with a few lines in one episode, and that in a role that could be considered quite a stereotype for Asian women in Western fiction.
It is possible (although it seems unlikely) that the fusion of Western and Chinese influences in the show came from a genuine desire for diversity, one that fell apart when casting and networks became involved. But as the show stands, without any East Asian figures playing a part in the world, that "diversity" becomes simple appropriation, taking elements of Chinese culture in order to add "coolness" to an otherwise Western world, rather than presenting it in an authentic and organic way. Firefly will take your Chinese characters, shadow puppets and swearwords unknown to most American viewers, but your Chinese people are not welcome along with them.
And that's a shame, because as a show, Firefly is generally well-written and very enjoyable. It's witty and engaging, with a wide range of loveable characters and some wonderfully written episodes. It's definitely a show worth watching. But considering how much Joss Whedon talks up his diversity and "strong female characters," and the amount of feminist street cred he's earned as a result, Firefly just doesn't pass muster.