For one, she lied about being Native American; even applied for law school under minority status in spite of a lack of evidence for her lineage. As a Native American myself (who has never tried to use being a minority as a crutch), I was offended that she would take advantage like that, and am not alone in that sentiment. I don't see it as any different than someone who has never been in the military claiming to be a veteran so that more people will respect them. She also lied about being the first nursing mother to ever take the bar exam, which I think is just a stupid thing to lie about. She has also publicly stated that she doesn't believe domestic terrorists should be stripped of their citizenship, which is a statement I couldn't disagree more with. I don't think those people deserve human rights, let alone citizenship.
I don't have many issues with her policy itself, besides her views on gun control, marijuana, defense spending, and animal rights (but pretty much any Democrat is going to have the same views on those issues). I just don't think she's very intelligent. I view her as the Sarah Palin of the left wing.