As you walk through your lighted rooms (preferably day light) see if the new coat has light spots showing the precious paint. This is call "bleeding through". This means that there's only one coat of paint or the paint was diluted or the trasition of colors were from light to dark (or the other way around) and primer was not use or the painter is inexperienced.
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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. House Painting Denver CO