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Surely the lesson to learn is:

DON'T PUT PASSWORDS ON HUGE DISPLAYS ATTACHED TO THE COMPUTERS THAT NEED THEM.

I don't disagree with writing them down. But put them in a book and lock the book away. Hell, I used to seal our "disaster recovery" password book such that anyone opening it would break the seal that couldn't be redone with damage. Then we put it in the company safe. Anyone slyly opening that to get the password would hastily put it back, and I'd know if a superior had ordered it open without my knowledge (for which I stated in advance, at that point I would be handing in my resignation unless there was a REALLY good reason, e.g. I was in a foreign country and uncontactable and a major incident, or if they were investigating myself for some reason, etc.).

Passwords are still passwords. Don't broadcast them on the same machines that require them. That's pointless. Don't whiteboard them at all. RAF places having them written clearly on bulletin boards? You're idiots. Distribute an internal email/memo to those who need them instead.

If you need to publicly advertise the password, you are effectively making that account unpassworded. That might even be a sensible alternative (if you can only access from the intranet anyway, and have to be logged in to do that, and it's just a hassle of yet-another-password). But you do have to consider that.

UK Data Protection basically says nothing that you can't write passwords down. But they have to be given only to those with need for them to carry out their duties. As such, writing them in a personal book or a memo in your (hopefully passcoded) phone is fine. Putting them on a noticeboard is not.