I'm not necessarily a strong embodiment of all the traits listed, but really, many of them are a pretty good description of either me or someone I know well at some point in our lives. So I wouldn't say they're inaccurate so much as overused and sometimes misused (which the matociquala does acknowledge somewhat). The essay made me think a lot about how these tropes relate to real people and to fictional characters, and I'm going to write out some of my thoughts on each of them here*.
Not like the other girls
Well, you've got two options when you're writing a female character. You can write her as a stereotypical female, or you can make her different in some way. The latter is probably going to be more interesting and more accurate/believable. Most real women are, in some way or other, "not like the other girls", it's part of what makes you an individual and (in fiction) an interesting character. Maybe we're physically stronger, or more fearless, or not into certain "girly things", or excel in a male-dominated industry. Sometimes we're even disparaging of other women who are more stereotypically female in ways we aren't (though in fiction that should be portrayed as a negative character trait). Where does the problem come? I suppose when there are too many characters who deviate from the stereotype in exactly the same ways, creating a new stereotype. There's also a problem when the author seems to have a very negative opinion of typical females, and writes atypical females to try to hide it.
Brittle and mouthy
Well, this trait describes many women I know, generally ones who I think are really awesome, but who can really get on my nerves if I have to work too closely with them for too long. The character trait can be a cover for minor psychological issues or be a reaction to the hectic nature of their lives. The problem comes when this these characteristics are pointless and poorly-written, and when there are too many female characters like this.
She starts out as an awesome female character, and ends up sidelined in favor of a male hero that she previously mentored. This gets listed as a characterization trope, but really, I don't think that's what it is. It isn't who a woman is, it's a thing that gets done to her in a sexist society. Portraying this happening in fiction isn't the problem - the problem is treating it as perfectly normal and unremarkable and okay. You should either show it as something unfair and worth fighting against, or you should rewrite to avoid it happening.
This one is straight-out unrealistic. If you're using this as a characterization trope, making your female characters either "dirty sluts" or "good girls", then you're doing it wrong. We're all more complicated than that. The only place for this in writing is in characters' minds, and then hopefully other characters will point out that they are wrong to think that way (or they will discover it on their own through experience).
Lack of female friends / only woman in the ensemble
Again, this happens sometimes in real life, if you're a woman working in a male-dominated field, or really into a hobby that many more men than women are interested in (going back to "not like the other girls"). But it is way overdone in fiction even when there isn't a reason for it, showing more men than women even when in real life there would be more of a gender balance. Sometimes when efforts have been made to even out the genders, they'll still fail by making only one woman a major role and the other females very minor characters.
I think one of the big lessons here is, don't defy stereotypes by creating new stereotypes. Write people as individuals, and watch how you write gender roles and gender balance.
* Note this is not intended as a rebuttal of the original essay. Some of my thoughts and opinions aren't too different from matociquala's, I'm just taking them and running with them.