Failure to obtain the necessary permits or to arrange obligatory inspections can be illegal. In some cases, if a project violates a zoning law or some other regulations, it may even have to be demolished if there is no way to comply with the law. A qualified remodeling contractor will be conscious of the permit process, and ensure that all permits have been obtained before initiating any work. You may want to add calling the contractor's suppliers to your list of follow up actions. This will help protect you from mechanics liens for nonpayment by the contractor.
Suppliers also can be a source to establish credit history for the company.
Your answer to that question should make the hiring decision a little easier.