If you're doing mystery shopping as a business, the IRS requires you to make a profit in at least one year out of every three (it could be 1 out of every 4 or 5 years). If not, they will consider what you do as a "hobby" and disallow most deductions.
Also, IC mystery shopping in general does not pay enough to cover expenses of running a business as anything other than a sole proprietor. C-corp, S-corp, LLC--these involve greater recordkeeping requirements, annual state fees, and even licensing requirements (with annual fees for that, too).
It might work if you combine mystery shopping with one or more related activities. Maybe.