I think that the area of "interview method" might necessitate a bit more clarification. There are different examples and approaches to this "interview method." One such way is the idea of one administrator interviewing a candidate with questions/ potential talking points and noting down answers. Another way is the panel interview, where different administrators or teachers sit with a candidate. Like all interviews, the advantage would be that the method allows for a wide range of solutions posed and potential areas explored regarding teachers and teaching. A potential disadvantage might be that teaching and interacting with students might be a career where "on the job" reality could be more compelling than anything else, and there is a value to the actual experience of teaching and learning which would surpass an interview. A potential way to address this could be to have a candidate actually teach a class to see how their approach is to teaching in actual circumstances. This is very arbitrary, but it might give a prospective employer an opportunity to see a teacher in action before making the official decision to hire.
Just FYI, the recommended answer length for this site is 90 words, so that is what you're likely to get. We can't write essays for people...
My view of the major "pro" of the interview method is that it gives the interviewer the best chance to find out what the prospective candidate is like as a person. This provides a clearer picture of how the candidate would fit in personally with other faculty and with the administration and students.
The bad side of this is that the interview does not really give any great insight into the candidates actual ability to teach. It is more of an indication of his/her personality and ability to answer interview-type questions.