This article with comments was terrific - it was so informative. I found the advice useful. It addressed specifics like the condition of the dry wall surfaces, any additional repairs such. pin holes, chalking, smoothing of wall surfaces, absorption of paint and number of coats that may be needed. It should also include insurance coverage, and reflect the clean-up afterwards. Having a written contract with the company's letterhead is a must.
Also, don't be afraid to ask if the painters are trustworthy people. Unfortunately, there are plenty of cases where a painter has stolen items from a home or caused damage to the house or injury to the homeowner. Subcontractors may not be as skilled as employees, and the contractor you're hiring may not have much experience working with them, making them more of a risk. Additionally, ask if the painters are employees or subcontractors, and what the screening or hiring process is like. If the company conducts background checks, that's a good sign.
I'm an architect and my firm routinely specifies interior finishes for projects so I thought I'd contribute a professional's perspective on the issue of how many coats of paint are deemed "acceptable". The fact of the matter is the average consumer usually isn't a paint expert and can't be expected to know about all the factors that impact coverage. That knowledge is considered "means and methods" and in a court of law, the responsibility lies with the painter or general contractor, not the consumer. What the consumer should be concerned about is the final result-does it look good and is it what you expected? The simplest way to communicate this to your painter is to stipule in your written agreement that the number of coats will be "as required to cover". That way all the guess work about what kind of primer, how many coats, how color affects the scope of work, etc., is removed from the consumer's responsibility and resides where it belongs-with the professional. In the contract that's why retention is always a good idea-typically 10% is withheld from payment until the job is completed to the satisfaction of the customer. Of course in return you as the customer have to be reasonable about what constitutes a completed job. Just my $.02.