When new versions of TeXShop are introduced, most folders in ~/Library/TeXShop are not changed because these folders store files created and edited by the user. But the Inactive folder is updated because users should have the latest versions of these items. This update adds new files and folders and modifies existing files and folders, but it does not remove files or folders no longer needed. I'm thinking of changing this behavior so Inactive is completely "cleaned up", but that is a more drastic step that needs to be carefully considered. In the meantime, users can accomplish that complete cleanup by removing the Inactive folder and letting TeXShop recreate it.
Since tex4ht can output MathJax calls, the mathematical formulas on the web pages it creates are essentially perfect. But the illustrations are sometimes distorted. Recently I read a brief note by Michal Hoftich, who maintains tex4ht, explaining how to fix this problem. So TeXShop 5.22 installs a new folder, ~/Library/TeXShop/New/Demo-Additions-5.22, containing a Read-Me file explaining the very simple modification to the Demo document which fixes illustrations. These Read-Me changes can be made in the same manner to other documents typeset by tex4ht.