Are they insured?
You should ask to see their certificate of liability insurance and workers compensation for employees. You don't want any nasty accidents on your policy.
If you are employing a company, are they bonded and do they carry out background checks?
How reliable is your company? You are busy, and you don’t have time to wait around for umpteen changes in time from your cleaning company. Ask your cleaning company how they measure their reliability, and do they ha