Workin in HR I agree with pretty much everything everyone has said.
I would also ask what the turnover has been for this position- might indicate a problem with the position or with management. Or why the incumbent is leaving the position- was it because of promotion, terminiation, retirement, resignation?
I would also ask to see at a later date the entire company (or at a very least your work unit) so you can get a sense of what they do and how they do it. I once worked as a recruiter where we interviewed in these beautiful offices and then you worked at work stations with chairs literally duct taped togther! Realisitic job previews cut down turnover for the company and prevent you from taking a job you would hate. Sometimes you walk in to meet the new co-workers and they are angry because they thought "Bob" should get the job. While you can work around that- do you want to if they are a tight clique you might be on the outside.
I just did a youtube video on top 10 interview tips because most people know the big things but little things like planning 2.5 times the amount of time the interview is scheduled for is not somehting most people think of or do!