Safest way to ensure that everything is fair is to get it ALL in writing , signed by both parties. Specify each item that needs repair. Also, BUY the paint YOURSELF. That way, there is no incentive to water it down, and you KNOW that you are getting the grade/quality you actually purchased. Don't be penny wise and pound foolish; if you are paying to hire a painter, buy the best paint that you can afford, to ensure maximum life of this home improvement.
We had a bad experience with an interior painter years ago, with the crux of the problem being him overcharging us at the end for "extra work" he didn't anticipate. One thing I'd strongly recommend is making sure it's in the contract that any additional work or growth work is estimated and communicated to the owner as soon as it is identified, otherwise the owner is not liable to pay it at the end.
The Lead Renovation, Repair and Painting (RRP) Rule establishes requirements for firms and individuals performing renovations, and affects contractors, property managers, and others who disturb painted surfaces. It applies to work in houses, apartments, and child-occupied facilities (such as schools and day-care centers) built before 1978. It includes pre-renovation education requirements as well as training, firm certification, and work practice requirements.