Nichola Stott outlines 9 things webmasters should check for a mobile-first index, including mobile handling, HTTP/2, front-end optimization, tag management, structured data, service workers, URL hierarchy, content experience, and journey experience. Checking these areas can help provide a great user experience for mobile users and improve site speed, which can reduce abandonment rates and help sites rank higher in mobile search results. Stott emphasizes the importance of testing sites using a device lab to avoid making assumptions about mobile performance.