Is this an addition or a replacement? What are the circumstances?
You already may have asked this question of a screener or during a telephone interview, but it's an important question. Really listen carefully to the answer here. If you hear, "Well, we gave the guy six months to get it right and he couldn't do it—and he was the third one in a year. We'll keep churning them until we get it right," you have a challenge ahead of you. If you hear, "We promoted the last two people out of the job," you will feel differently. If you hear, "Well, the job doesn't pay that well, so people leave it after two years or so," it may still be a good job for you, but likely you'll be there two years or so.
This is one of the best questions you can ask. It could give you real ammunition to help you sell yourself. For instance, if you hear "We wanted the person in the job to take more graduate courses so we could promote him, but he just wasn't motivated," you can sell your desire to further your education. Just listen and take notes. You may want to feed this information back to the hiring authorities.
What is the most difficult part of the job?
This might be a question you save for subsequent interviews, but if things are going well in the initial interview, it can be a great question.
The answer can "load your shotgun" so you can sell yourself better. It also can tell you the greatest challenge you may have with the job. An answer like, "It's working for me, and I have a real reputation to live up to... ha!" (don't laugh, I've heard it often) might give you the opportunity to mention that you have worked for some of the most demanding bosses. It might also tell you about the ego you are interviewing with. Or it might tell you to run away. If you hear, "It's keeping up with the accounting for nine different subsidiaries and getting the reports out on time," you will want to mention where you have done that kind of thing before.
Initial Interview Question Mistakes
One of the biggest initial interview mistakes people make is to ask questions that either put the hiring authority too much on the spot or ask questions that expose sensitive issues. A question like, "In doing my research, I noticed that you had to restate your company earnings the last year. Can you tell me what the circumstances were for that?" might be a good question and one you would want to know before you might take the job, but you don't want to ask a question like that in an initial interview. Or, something like, "I see the company has lost money and contracted the last two years. What happened?"
Stay away from uncomfortable questions like that, at least in the initial interview. It may show your business acumen but now is not the time. As you become a finalist for the position, or are offered the job, there will be plenty of time to ask these qualifying questions. In fact, most astute employers will expect you to ask them. But do it at the right time. And ask the right person. Asking a screening H.R. assistant about the company's involvement in a lawsuit isn't smart. Now, asking the V.P. of finance about that kind of thing as you are being offered the job might be a good idea. You need to know what you are getting into and how it will affect you.
Remember that your purpose for asking questions in an initial interview is to sell yourself to the next stage of the interviewing process. Don't qualify yourself out of what might be a good opportunity by asking too many of the wrong kind of questions in the initial interview.
You will notice that I don't recommend asking any "what's in it for me" questions in the initial interview. Questions like, "What kind of money is associated with this position?" are not good questions for an initial interview. Now, if money or benefits come up in the interview, go ahead and address them, but don't delve into them much at all. There will be plenty of time for that in subsequent interviews. You want to sell yourself to the top of the candidate stack. Once you are there, most everything else takes care of itself. If the money isn't right, you don't have to take the job.
Take notes, and as you go through the interviewing process you can get clarifications on things you don't understand. You don't have to know everything right now.