When you use SharePoint Designer 2013 with Service Pack 1 to open Office 365 SharePoint site then you might have the error:
Server Error: The version of Microsoft SharePoint Foundation running on the server is more recent than the version of SharePoint Designer that you are using. You need a more recent version of SharePoint Designer
You check you SharePoint Designer 2013 with SP 1 is already the latest.
I resolved this by Sign Out the user and Sign In again to the right user.