So why not just paint your own home. I'm not a painter, so my wife and I take our time, buying the paint and supplies, and doing our own painting. Yes, we need to tape, and it's not perfect, but we get the satisfaction of seeing our completed work. Get the supplies, sliders for your furniture, and patience and go for it. That way YOU have control over the entire project.
Just like with roller paint application, painters are not limited to using just one stroke when cutting in. It is important, however, to work towards the edge of the corners applying even pressure. If time permits, painters should allow their cut in work to dry completely before applying paint with rollers, keeping in mind that light touchups on corners and edges will always be required at the end.
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.