Experienced postdocs and advisors suggest the following questions be asked of (and about) a prospective advisor:

• What are the advisor's expectations of the postdoc?
• Will the advisor or the postdoc determine the research program?
• How many postdocs has this advisor had? Where did they go afterward?
• What do current and past lab members think about their experience?
• Will the advisor have time for mentoring? Or should I seek out other mentors?
• How many others (grad students, staff, postdocs) now work for this advisor?
• How many papers are being published? Where?
• What is the advisor's policy on travel to meetings? Authorship? Ownership of ideas?
• Will I have practice in grant writing? Teaching/mentoring? Oral presentations? Review of manuscripts?
• Can I expect to take part of the project away after the postdoc?
• How long is financial support guaranteed? On what does renewal depend?
• Can I count on help in finding a position?
• Will the advisor have adequate research funds to support the proposed research?

Source: Enhancing the Postdoctoral Experience for Scientists and Engineers