How to handle damp and moldy walls during old house renovation before repainting?

When renovating an old house, you cannot simply scrape off the mold and repaint damp walls. Cleaning the surface will only look good for a while; if the source of the moisture isn't addressed, it will return in a few months. I once worked on a basement wall where the previous contractor just scraped off the mold, applied putty, and used anti-mold paint. The corners turned black again shortly…