Mold spores are the reproductive offspring of moulds. They cause allergic reactions in some people and simply killing them is insufficient to keep them from causing these reactions. They need to be completely removed. Mold spores need to be killed with a biocide and then scraped away.
Purchase a solution approved for killing mould spores, such as Tilex Mold and Mildew Remover, Formula 409, or DepHyze. According to the Intl. Union of Operating Engineers, benzalkonium chloride (an ingredient in Formula 409) kills mould spores.
Soak the mould with the solution thoroughly BEFORE scrubbing. Scrub only as deep as the mould is soaked. This prevents sending dry spores airborne. Resoak the mould after each layer is scraped away. Discard the wet mould in a sealed plastic bag.
Soak the wall thoroughly one final time after the mould is all scraped away, just to kill what you can't see. Keep it soaked for 15 minutes. As soon as that application is dry, apply spackling paste with a long spatula to smooth out the surface and keep any remaining spores from going airborne. Then prime it for an additional layer of protection, whether you plan to paint it or not.
Ozone generators can also kill both mould and mould spores. However, the machines cost hundreds of dollars and many on the market don't produce the concentration needed to overcome ozone's fast rate of self-degradation.
Use a disposable face mask so that you don't inhale spores during the scraping process. Use goggles to apply the antiseptic. Keep a pail of water handy in case you get any solution on your skin or in your eyes.