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.
This is an area that interior painters can easily cut short to save time. Most contracts don't state the extent of the wall repairs included, so it's up to the painter's discretion how much they will do. If it seems like too much work, they'll usually point out the repairs but don't include it in the bid. They'll then ask you if you'd like it fixed after they start your project and let you know how much more it will cost.
This was very helpful. I wonder if i would really follow through and check to see if my painter was cheating me. I used a painter I found on Angie's List. This was 5 years ago. He did a great job. I know he did patching only for about a day and a half. We decided on the kind of paint before he started. that is what he used. I don't know if I could stay on top of him and watch him open every can of paint.