To my understanding, you should always have questions. The purpose of them offering, as I understand it, is to give you a chance to show your initiative, inquisitiveness, and that you did your homework and have deeper interest than can be answered with superficial web info. One good one would be about the size and character of the working team. How many people would you be working with, from what different departments. Another is what are the most important concerns of the supervisor with respect to the specific job. (I had a technical focus question in my field -- not sure what type of job you're going for, but the question would relate to the particular critical job duties. There must be places where a bad employee screws up and a great one shines. What skill area is that?) Another: What are the most difficult challenges in this job?

Personally, I think any polite question that helps me know in advance the worst that's going to happen is also useful for me personally. And they are usually not going to reveal that without asking. They're going to put on a happy face.

I'm sure there are other good questions to ask.

Well, I agree, they do ask some really dumb questions, too!