PROBLEM: Deafult.aspx is not opening in the SharePoint Designer
Error Details
Soap: Server was unable to process request. A Web Part or Web Form Control on this Web Part Page cannot be displayed or imported because it is not registered as safe on this site. You may not be able to open this page in an HTML editor that is compatible with Microsoft Windows SharePoint Services, such as Microsoft Office SharePoint Designer. To fix this page, contact the site administrator to have the Web Part or Web Form Control configured as safe. You can also remove the Web Part or Web Form Control from the page by using the Web Parts Maintenance Page. If you have the necessary permissions, you can use this page to disable Web Parts temporarily or remove personal settings. For more information, contact your site administrator.
Solution
The problem is that the default.aspx page may contain some error web parts which can be removed by hitting the following url
This will open the web part maintenance page. So, here you can delete the error web part.