When verifying a tenant's employment, rarely do you want to start by calling the employer/supervisor that the tenant listed on the application. You might want to start by looking up the company's name in the phone book or online and calling the main number, requesting the Human Resource Department. It is sad to admit, but many of the tenants that you are NOT interested in having, know to enlist their friends to pose as a referral for both their jobs and previous landlords.
Usually in larger companies, Human Resources is the only department able to provide employment information and then they can only convey very limited information. They are apt to tell you that the employee does works there, and how long they have worked there. If you ask your questions correctly... "His application indicates that he makes $XXXX. Can you confirm that?" You might get better answers. It would be nice to know if the employee is there as a full time employee or under contract and if they know of any reason the employee may not continue with the company. As much as you may want to know about incidents, complaints, and work styles, I doubt you would get any of that information.
Be sure to check previous landlords carefully as well. If the home is privately owned, see if someone can find the property owner's name from the tax records for you to confirm you are talking to the right person. You will want to know if the tenant paid on time. Ask them if they would rent to them again and why they are leaving their current place.