I've built email notifications into the major stuff, so on failure, my bot sends them an email with the error message. I've got my address in the reply-to. So they reply "please advise" and hit send.
For the minor stuff... a copy-pasted error message from the UI is luxury, you're right.
I don't know about your work but there are tools/libraries to instrument your applications. For native applications there are things like ABRT, for web applications there's Sentry and a lot of other tools.
People notify you that something didn't work? What a treat! For me the work just doesn't get done, and you have to ask why before you get an explanation that there is some technical blocker.
For the minor stuff... a copy-pasted error message from the UI is luxury, you're right.