If you receive error messages from Google when trying to open the Google Webmasters Tools/Search Console integration, ensure that the account used to login to Google is the same account associated with the website domain in Google Webmasters Tools/Search Console and that the domain specified is exactly the same registered in Google Webmasters Tools/Search Console. The domain must match exactly, so if you have registered http://www.mydomain.com and your are requesting for example http://mydomain.com Google won't allow the access.
In this case you could receive an error message: '(403) User does not have sufficient permission for site 'http://www.sitexyz.com/'
You can set preferred domains for Google Webmasters Tools/Search Console (and Google Analytics) in the component configuration section as visible below:
Also if you are updating from a previous version and you already have an ongoing login to Google used to access the Google Analytics stats, you must logout and perform a new login. This is required because now the application needs permissions for both Google Webmasters Tools/Search Console and Google Analytics.
Finally, if you have setup your own Google Application ensure that both API for Google Webmaster Tools/Search Console and Analytics are enabled in the Google console.
If you are using the new Search Console to add a new property, ensure to use the 'URL prefix' method to register and verify your website. Indeed if you choose the 'Domain' property method based on DNS, the Search Console API won't work and you will continue to see the above error about missing permissions to access the requested site.
As a side note, after an update from a previous version, it would be ideal clearing the browser cache to have all the panels used in the Google Webmasters Tools/Search Console dashboard expanded automatically by default.