Drywall ceiling was painted, then some time later it was pop corn textured. When removing the pop corn, the paint under the pop corn is hard to scrape off. When repainting over the old paint, the old paint peals back all over the place. What can I do to get the old paint off so I can mud some of the dings in the drywall and repaint it?

The only right way is to scrape and sand the old finish back to the drywall base. Not easy and some people have used 1/4 drywall over the old ceilings to get a good base. You can possibly rent a Porter Cable drywall sander. It has a rotating head sander and vacuum system and would probably accomplish the task.

I own a rental property with popcorn ceilings. I'm dreading the day if I ever have to remove that stuff! I did look into it though... just in case. I was told the popcorn is water soluble. So, you need to scrape as much off as you can dry with a variety of putty knives, then dampen the reside and carefully scrape the remainder off being careful not gouge the drywall paper surface. Once it's dry it will still need a sanding to totally remove all traces. I was also told it's very messy and you should empty the rooms of furniture and spread tarps to protect the flooring.