As an admin user you can make all future punch list items private by default. To do so, click on the 'Configure punch list settings...' in the bottom right of the Punch List log page. From this page select the 'Punch List Items Private by Default' checkbox. See Configure Advanced Settings: Punch List to learn what other settings you can configure for your punch list items.
This will make all future punch list items private, but will NOT retroactively mark your punch list items as private. If you want your punch list items to be private, we recommend you do this at the beginning of a project.
Private punch list items can only be seen by 'Admin' level users on the Punch List tab and those included on the punch item of the project.