There's also some loosened tape at one joint where a leak once occurred. The roof has been sealed, as has the area on the ceiling side, with no more problems--just the loosened tape. Should the tape be replaced, should compound be applied at the indented areas of the ceiling, would it hold onto a slightly textured existing surface or would brushing or rolling on a textured paint as is the best solution? Spraying on something would be too big a mess. Any suggestions would be appreciated.

The tape should be scrapped off with a sharp putty knife so you have a clean edge that is tight. Reapply compound and wet sane, then prime before applying your texture

Is it possible to fill in the indentations at other joints and dimpled nail sites in the ceiling before applying a thicker texture over all of it? Would compound adhere? Repairing the damaged tape will be tricky, since the rest of the ceiling has a brushed-on texture that I tried to match before. It didn't work very well.

Your repair will be less noticeable than the loose tape you have now. Texturing a ceiling requires certain tools and brushes, ever doe any texturing before or seen it done?

The texturing was done 38 years ago and I don't remember how it was done or know if it's still done the same way. I attempted to imitate it when I did the patch job and failed miserably. Still, the loose tape is just along part of one seam and I'd still like to know if compound would adhere to the other visible seams and nail dimples that show, in spite of the texture. Also, even if I replace the loose tape in that one area, I assume I'll need to remove the sand finish texture there so the compound and tape will stick to a flat surface. Then, I figure I'll need to resurface the whole thing to make it uniform. That's where I'm wondering about using a slightly heavier texture. I realize I may have to call in a pro who's used to working overhead.

You need to scrape the loose tape off, apply new tape finish it sand it and retexture it and prime and paint if you can not match textures call a professional. Remember if you can't do this and try to fix it yourself it could cost you more in the long run

Any thoughts on whether compound would hold on indentations from nails and along seams (unrelated to the loose tape issue)?

Joint compund is fine for nail dent and imperefctions. Apply one coat with a compound knife and then do a second application feathering so the nail dent patch is the size of an apple. Once its dry wrip with a damp spong and finish feather, don't use sand paper or screen

Okay. Just to clarify--the surface is the "sand finish" rough ceiling which has been painted in the past. Will the compound still stick?

Yes but you must scrap away a patch of sand before you apply the compiound. If you don't remove the sand your compound will be thicker than descired and stand proud of the rest of the ceiling. Reapplying sand will be your last step