Most of the tape in question is on the roof. The roof has blown texture, and it does appear that the tape was not covered by another layer of drywall.
Please provide a little more info on the tape. I'm familiar with the paper tape that was originally used. I'm assuming this does not need adhesive?
I have also seen a fiberglass mesh tape with adhesive on the back. This tape has about 1/8 or 1/4 inch rectangles and the fiberglass filaments are very thin. This tape is about 95% open. Is this the fiberglass tape you are recommending I use?
Another question regarding the roof. I recently had a new heating and a/c system installed in the attic. I think all of the walking around up there caused some of the tape to lose adhesion. We use the attic for storage, and I put down 3/4" plywood over the boards. I am heavy and my wife says you can see the ceiling deflect some when carrying or moving around boxes in the attic. Based on that, am I better off with paper tape or fiberglass tape?