While working with SharePoint Designer and opening sites in Office 365 I came across the below cryptic error message.   The root cause is lack of permission.  Granting SCA fixed.

Cheers!

Error

After opening URL SharePoint Designer client displays “The version of Microsoft SharePoint Foundation running on the server is more recent than the version of SharePoint you are using. You need a more recent version of SharePoint Designer.”

Resolution

While unclear, the above is actually a permission denied error.   Grant the user account more permissions, such as Site Collection Admin (SCA), and you will connect OK.