Level of confidentiality about current company and interviewing

[Nikia]

Next week I have an interview for a somewhat higher level position. At this interview as with previous interviews for such positions, I am sure that I will be asked questions that this might be an issue. Even in answering questions like "What have been your biggest accomplishments? and "What are some important problems that you have solved?" "Have you ever dealt with...?" concern me a little bit. Perhaps, I am becoming more paranoid about this because I realize that not only could I make my company look bad to this other company but I also might not be hired because they consider me unprofessional by revealing too much. You must realize that I work for a relatively small food company in quality assurance and most of the problems that I deal with involve food quality and food safety issues. Is it appropriate to really answer these questions honestly? Is answering them honestly really no big deal? Does it matter if this company is a competitor, customer, or supplier or if the company has no dealings or potential dealings with my company? I never signed a non disclosure agreement. I guess that if it is a company that has no dealings with my company, I am most concerned about the appearing professional issue.