1. What will be my key priorities for my first few months on the job?
The answer to this question will tell you a lot about the day-to-day challenges and constraints of the role you're interviewing for. Bear in mind that this one can easily be turned back on you - the interviewer may ask you for your own ideas of what the key priorities should be. So have an informed answer ready if you plan to ask this question.
2. How big is the team, and what other teams will I be working with?
Not only does this question reflect well on you, helping to convey your team-player credentials, it can also help you to learn more about the kind of working environment and people that await you should you get the job. This enables you to judge whether you would get along well with colleagues and fit in with the organisation's culture.
3. What could I do to contribute to the success of this organisation / department?
This is the question that business owners and your interviewer have probably asked themselves often enough, so hearing it from a candidate creates an instant connection, signifying your seriousness about furthering their deepest wishes for the organisation. It communicates a genuine wish to assist your employer with their own aims.
4. I recently learned from X that Y is happening. What impact will this have on the business?
It's always good practice to read up on the organisation you are seeking to join prior to the job interview (as well as wising up on the industry rivals and what they are doing). Knowing this information will enable you to ask informed questions like this one, thus marking yourself out as having a real interest and understanding of the department, company and wider industry.
5. What are the qualities needed to excel in this role?
This is a direct appeal to the interviewer to outline once more their most pressing priorities for the vacancy, perhaps allowing you to expand on areas of your own strength as a candidate that weren't touched on during the main interview. It's a great question to ask in a job interview as it allows you to direct the conversation, especially if you enquire about the importance of a certain characteristic and the interviewer responds in the affirmative. This gives you an opportunity to describe your qualifications in that area in greater detail.