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.
These are some fantastic questions to ask and I particularly like the one that is concerned about safety for the painters. After all, if you have a large home and you’re hiring them to paint the exterior of that home then they’ll likely be on scaffolding. Because of that, you need to make sure that the contractor not only provides appropriate safety training, but has the correct liability insurance as well.