OK, I haven't posted in ages. I'm not going to go into what's happening in my life, but I read another post on LJ, and wanted to do an extended response, so my own account sounded like a good place to do so.
I can't believe this. The thing is, most of these character interactions could have been done just as easily by reversing the characters' gender (with the exception of Inara). As a fan of the show who really doesn't like it when people read all kinds of messages into what is supposed to be good entertainment, I will now issue a point-by-point rebuttal.
First of all, when Zoe calls Mal "sir" it's because he's her commanding officer. Zoe's deference to Mal is that of a private to a sergeant - their original relationship in the war. That is the only reason she defers to him. I have a better way to describe Zoe than an Amazon: infantrywoman. She's not just a soldier, she's infantry. Front lines, boots on the ground, you get the idea. That she's female, yet dominates her husband, is a feminist twist - it shows that a woman can be in charge of a relationship. As for the racial part, I can't see how that plays in. It isn't a major part of Zoe's character that she's black. While Joss may have decided that having a black second in command would balance out nicely, I have an alternate theory as to why Zoe is black: Gina Torres is black. Moving on.
The "duct tape" comment. Mal is joking here. Kaylee's humor and cheer can be so annoying at times (from there perspective) that you want to "duct tape her mouth shut and throw her in the hold for a month". It's a rather offhand comment anyway.
Next, Inara. OK, first, I take issue with the whole "most sex is rape" thing. It assumes that women mostly have sex due to pressure from the man, for one thing - as opposed to having their own sexual urges. And it's quite clear that Inara does consent to sex - otherwise, she wouldn't have become a Companion.
As for why she would become a Companion, that's worthy of some discussion. Assume, for the moment, that you are a young woman living on an Alliance core world. Why would you want to become a Companion? I do agree that the constant sex can't be an attraction - otherwise, a lot more women would be prostitutes. But the glamour and money would attract people. Why do so many girls want to become movie stars, or models? You might argue that this objectifies women in Alliance society. I'd agree with you. But that's a problem with Alliance society, which is hardly shown in a positive light. If anything, that the corrupt, moneyed culture of the Alliance glorifies Companions might be a feminist point Whedon is making - if the bad people do it, it must be bad.
I do admit that it doesn't make so much sense for Inara to become a Companion. She clearly has business smarts - she could make a decent living as a businesswoman in a more "conventional" field. My best guess is that as a Companion, she makes a lot of money. In "Shindig" Mal comments that Atherton must be rich to afford Inara's rates.
And then there's Mal's treatment of Inara. Throughout the show, he calls her a whore, intrudes upon her personal space, etc. There is a very simple reason: Malcolm Reynolds is an asshole. He isn't perfect, he's an anti-hero. It's part of his character. I imagine that Jayne would act the same way, though we don't see much of Jayne and Inara together. Probably because Inara avoids Jayne if she can. Wash, Simon, and Book, on the other hand, treat Inara with the respect she deserves. Because they're not assholes.
Finally, there's her "servicing" of the crew. When people come to Inara for emotional support, that's not her servicing them. That's her helping them because they need help, and Inara is a nice person who knows a lot about human psychology, and can often provide helpful advice. And her "servicing" of Kaylee is simply two women playing with their hair, just having fun.
And while it is unfortunate that you have not known a healthy relationship between a white man and a black woman, that doesn't mean they don't exist. But more to the point, I cannot imagine Wash abusing Zoe in any fashion. There's the slight problem that Zoe could easily kill Wash if it came down to it. Not to mention, Wash is something of a pacifist (he always suggests the nonviolent approach).
I'll also try to cover a few things you didn't go into, but that seem logical for you to cover in your mind. If you didn't have problems with these, I apologize. "Our Mrs. Reynolds", for one. I can see where you might think that Saffron is basically a caricature of strong women as lying, cheating, conniving bitch. But I don't see that. I see Saffron as a lying, cheating, conniving bitch. Basically, she's an evil seductress, a well-known villain archetype.
And finally, there's River. One possible train of thought you didn't mention was how River, the helpless little sister, needs her big brother to protect her. This was the situation at the start, but I think that there were signs that River was a changing character - had the show continued, she would have become a strong person, and regained her sanity. Most notably, in "War Stories" River kills three men with her eyes closed, and in "Objects in Space" she outwits the bounty hunter.
You didn't make it clear if you had watched Serenity. In Serenity, this transformation, which was probably intended to be a slow one, taking a season or two, was accelerated, and made the focus of the film plotline. The climax is where River Tam, previously the helpless, tortured, insane girl, goes toe-to-toe with a horde of Reavers, and kills them all in a beautiful fight scene. If you wanted to interpret that in a feminist perspective, I'd say that the Reavers, bloodthirsty and savage, are the masculine, while River, graceful and strong, is the feminine. And then the feminine side goes and kicks the masculine side's ass.