What is the consultants SEO Process? What can you expect in the next month or months. If they can’t explain it to you, don’t hire him
What is the first he would do on your site? Look for some sensible recommendations that show they've put in some time researching your site.
How are results reported? Traffic matters more then rankings.
Who owns the copyright? Ideally you are buying the rights to everything thus giving you an asset you can take with you.
How long will it take to get results? Ideally results can be shown within 3-6 months. If they make claims about getting results sooner don’t use them.
How long do you work with clients typically? Hopefully you are paying for a partner and consultant and they will continue to work with as your business evolves and as the web changes.