Ask for and check "specific" references. Specific meaning, how long ago was the reference job done and what specific type of painting work was done.

Ask for proof of liability insurance (one million dollar minimum) and workmen compensation insurance by getting a copy of their coverage faxed or mailed to you directly from the insurance company. Why is this important?

Ask for the company's payment policies. Never give any money until your job is completed. Why this is so important?