Before I say a word, let's get this out of the way: regardless of what she says, it is never okay to harass somebody for disagreeing with you, and especially not okay to issue rape and death threats. That is beyond not cool, and is something that we as people who love video games should all be ashamed of.
Moving on: I don't care much for Anita Sarkeesian. On one level, this is a very simple matter of I don't find her video style particularly effective. They're very rote and mechanical feeling, as if she wrote an academic paper, toned down the academic speak, and read it into a camera. It's not a very compelling style and doesn't do her any favors in communicating her message, and given the wild success of her Kickstarter, is notably low on the production value spectrum. She raised a lot of money for this series; invest in some video editors to inject a bit of style and flair in your series, please. It'll do wonders for those on the fence about your message.
On another level, however, I am not the biggest fan of her specific message. While I am absolutely all on board for pointing out the inherent misogyny in this industry and its trends, I am not entirely sure that Sarkeesian is doing the best job at it. There is value, I think, in pointing out the prevalence of the damsel-in-distress trope in video games. However, I think it is also critical to note that such a trope is present in society at large, and is not a problem exclusive to video gaming. This is my primary point of uncertainty regarding Sarkeesian's actual message: she's pointing out misogyny in society at large, but presenting it as something unique to video gaming. This is damaging to the reputation of video games, making it appear that it is the only industry with such representation problems (it's absolutely not). It places the onus on society rather than on gaming culture, making her claims something easily deflected to "this is just a problem with society, not games specifically," which makes it easy to ignore the very real problems that gaming has that are unique to this industry.
In summation: I think the work she is doing is valid and important, as we don't have enough female voices in gaming today, but I think it is slightly myopic in a weird way by not highlighting gaming's very specific brand of misogyny, and I also think it is being delivered rather poorly in her videos, which lack a compelling style.