Follow-up of #2040 which changed the expected behavior for site builders/admins. Since it is likely to upset a portion of users (the ones that are using Backdrop to build and maintain sites - these are the ones we are trying to get to adopt Backdrop), it'd be best to follow up with a more solid/intuitive solution:

I think that when error messages are disabled, showing an error badge in the admin bar would be gold for site admins. We'd be putting existing, recently added functionality (badges) to good use and upsetting admins less with our choice of end-user-favoring defaults.

GitHub Link: 
https://github.com/backdrop/backdrop-issues/issues/2138
GitHub Issue #: 
2138