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.
I agree with JHs. If there is no new color on it at all, just talk to the painter about it, if it was an honest mistake (which can happen very easily while painting) your painter should have no problem fixing it. However, in my years of experience, it is not unusual for 2 coats of door paint (good quality) not to cover very well at all. I once painted a red door 7 times, plus a tinted prime coat before I found the door to be a solid color.