You guys have been great. Thanks for all the answers to my questions.
A quick summary: Due to problems with the original taping on my drywall, I had to remove all of the popcorn ceiling and replace tape joints. I also discovered a poorly done repair which I had to redo.
I removed all of the damaged drywall and installed a new piece. I went into the attic and used a 1x4 to put drywall screws into so I would have a solid joint. On the bottom side, I used two strips of the 6" wide fiberglass mesh tape over the patch to insure the repair held.
The patched hole came very close to two tape joints that came together at a right angle. I used fiberglass mesh tape on the joints also. In making the repair and fixing the seams, the drywall mud from both repairs ran together, so I ended up with a large area with a thin layer of mud.
With me being an amateur, it appears to me that it is easier to wetsand the large area than to work a bunch of individual seams and nail holes.
Is there anything wrong with applying a very thin layer of drywall mud over the entire ceiling? I did this to about a 3 ft x 3 ft area, and the roof was smoother than another similar area where I just fixed all of the individual spots and tape seams.
Cost of the mud isn't an issue, and I think it goes faster if I lightly skim the entire area. What do you guys think? Any problems with this approach. I will probably just paint the roof and apply the popcorn ceiling sometime down the road.