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This is Tim with Microsoft Office 365 SharePoint Support.
Have you recently changed your domain to point to a custom domain rather than the default address that you were provided with your subscription? If you have it will take some time for all the changes to propagate before you will be able to edit your public-facing website.
I will continue to monitor this thread if you are still having issues.
Microsoft Office 365 SharePoint Support
I am also having problems - I changed my sharepoint address to the custom domain last night. I want to correct some areas of the web page and am unable to edit it - browser can't find the link that is shown when I hover over edit website. suggestions???
Did you try to edit the public-facing website soon after changing from the .sharepoint.com domain to your custom domain? There is a propagation period that you will have to wait before you are able to make the changes.
You can also try to append your domain with /_layouts/wh/Editor/default.aspx (http://www.<domain>.com/_layouts/wh/Editor/default.aspx). This will launch the in browser editor.