3. But most importantly (at least in my book), can you get along with this person. I have seen way too many sad situations where the mentor and the student are simply either miscommunicating with each other, do not understand each other, or simply cannot get along. This will make for a hellish experience and I have never seen anything good coming out of such a thing.
Looks like I'm not the only one who feels this way. In the latest issue of Science's Careers section, there is an article on choosing a research adviser that highlights the same issue.
It's both legitimate and wise--indeed, essential--for aspiring scientists to evaluate a prospective adviser before committing to spending the next 4 or 5 years in her research lab. A hasty decision can mean years of dissatisfaction, and poor advisory relationships are a major reason why students drop out of graduate school. Signing on with an adviser who isn't a good fit, or who isn't sufficiently attentive to the development of students' technical and professional skills, can also hinder your chances of landing choice jobs.
Read the whole article. It has several very good suggestions on what one should do in choosing an adviser.