The presence of black areas on walls and ceilings near nails and stud/rafter boards, despite not being mold, indicates a potential issue with rust or staining bleeding through the paint. To address this concern effectively and prevent recurring discoloration, the following steps can be taken:

1. **Preparation**: Prior to repainting, it is crucial to thoroughly clean the affected areas using a mild detergent solution to remove any dirt, debris, or grease that might be contributing to the problem.

2. **Priming**: Apply a high-quality stain-blocking primer specifically designed to prevent bleed-through from rust or staining, use 2 coats of a Pigmented Shellac Sealer Primer. This acts as a barrier between the substrate and the paint, ensuring that the discoloration does not resurface.

3. **Multiple Coats**: To further enhance the coverage and durability of the paint job, consider applying multiple coats of paint after the primer has dried completely. This can help build a strong barrier against any residual staining.