I had the same issue/error where I cannot update any new configs on the System Administrator profile because of the error:
Permission Subscribe to Dashboards: Add Recipients depends on permission(s): Subscribe to Dashboards
The issue here is, with the latest Salesforce release(Summer' 18), there was a bug that rolled out, ie., disables the permission:
Subscribe to Dashboards for the System Administrator profile
But the dependent permission:
Subscribe to Dashboards: Add Recipients is still enabled. You can find these permissions under: System Permissions.
Even a System Administrator user cannot have access to change/modify these System Permissions. And without enabling the permission:
Subscribe to Dashboards, we cannot save any further changes on the System admin profile. Thus creating a Dead-lock situation as there is a mutual dependency where we cannot make any further updates.
Solution: We had to open a case with the Salesforce. The rep mentioned that they already identified this issue as many users have reported already and they can fix it by themselves. So within a day, the issue on our Sandbox has been resolved.