Really disturbing: I just managed to get my Mac into a state where it was displaying one user account on the built-in monitor and a different user account on the external monitor (and projector).

Given that I use a dedicated user account for teaching, I'm glad that I didn't have anything too confidential open on the private account, since there was no way to move the mouse to the external display to close it.

Once I'm not in a workshop I'll see if I can work out how to reproduce the issue.