Coating mud on paint tends to be another issue most all the time with Reno's, as paint doesn't absorb moisture with-in the second coat of mud.
You will find that there will be an overwhelming amount of air bubbles coming through the second coat of mud, and the most effective way to battle this I have found is to apply mud over the area and then wipe it right back off, this moistens the first coat over the paint and allows it to adhere better, then reapply the second coat immediately as normal.
This method will typically work in most cases, but not every time, sometimes the air bubbles are so bad you have no choice than to come back the next day and coat the area a third time, maybe even a fourth.
This is a major reason why big renovations are sometimes difficult to estimate, and can be more expensive and time consuming than your new build.
I've just scratched the surface, by mentioning two techniques required during renovations, their are many other things to consider that are a lot different than your new build.
This is why, as I said at the beginning, if your doing a large renovation, and your looking for a good drywall finish, which I'm sure you are, as over 80% of your home is covered with drywall, you will need to find yourself a quality company to do the work for you.