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.
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.
Thorough preparation is essential to ensure a good finish. Contractors might have to fill cracks or holes and remove old paint if it is badly worn, peeling or flaking. They remove all paint and apply a suitable primer to the bare surface. If the existing paint is in reasonable condition, they clean it and rub it with abrasive material to provide a key for the new paint. On new surfaces, such as bare wood or fresh plaster, they apply a suitable seal, followed by a primer coat.