What are the important questions to ask during an interview for an adjunct lecturer position?
Some other things you may want to ask, but unfortunately will probably be able to guess the answers to by yourself:


What is the compensation per period/credit? (I waited to ask this until after the whole interview, and it turned out to be so far below minimum wage I almost laughed when he said it. Thank goodness I caught myself.)
What is a typical class size? (To know how much grading you'll have.)
Do you have any materials from previous lecturers that I can use? (Save prep time)
Will I have access to a TA/student grader?
Are these traditional or non-traditional students? (You may be able to infer the student commitment to your classes with this answer)


It would also be a good time to ask about resources, parking, if you get an office or anything, and other administrivia.