Microsoft.BizTalk.ExplorerOM.PermissionException: Error in the application after upgrade to BizTalk Server 2013 R2

After upgrading to BizTalk Server 2013 R2 certain (service) accounts get this exception:

Microsoft.BizTalk.ExplorerOM.PermissionException: Error in the application

Running the BizTalk Server Administration Console using the same account you'll get this similar error:

Failed to load Group […BizTalkMgmtDb] data providers. (Microsoft.BizTalk.Administration.SnapIn)

Connecting to ExplorerOM failed. (Microsoft.BizTalk.SnapIn.Framework)

Error in the application. (Microsoft.BizTalk.ExplorerOM)

We saw the exact same problem back in 2013 when we installed BizTalk Server 2013. I've described a fix for the issue in this post:

http://blog.brandt-lassen.dk/2013/06/biztalk-administrators-database-role.html