Some proposals simply say to paint the walls and ceiling and never specify the number of coats to be applied. If the colors are similar enough, it's possible to get away with one coat of paint and not discount your pricing. No matter how hard you try, tiny, pin-sized air holes will pop exposing the original walls. This may not bother you if you can't notice it, but principally speaking you should have paid your painter less for the work.
As an owners rep and former estimator for a gc i do expect to pay a reasonable deposit say 10 percent and then weekly progress payments. I am asking the painter to book his time and to do the work on my schedule. Most painting companies are not huge operations they will pay their staff weekly. For most repaints i ask for one tinted primer coat and one finish coat for 100 percent coverage. New work gets one tinted primer and two finish coats for 100 percent coverage. The cost of the paint is not really that different for colors or finish. Brands like european fine paint and C2 are more expensive than Ben Moore and sometimes more difficult to roll based on their consistency. Some home depot brands are as expensive as the Ben Moore and of equal quality others aren't. Red paints are notorious for number of coats required and special priming requirements.
Over the past year I have had several jobs given to 2 Angie's list recommendations and 1 not from a recommendation. They all have one thing in common, lack of sufficient and correct preparation to save time, labor, and the fact that they put a person in charge that was a cut corners type of worker. The two from Angie's list sent worker/s back to try touch up problems, but once the job is not prepared correctly in the first place any extra work is like putting a band-aid on a dirty wound.