Prof's neurological health is declining rapidly. What can I (TA) do? I'm a law student acting as a teaching assistant/fellow for a tenured and notable law professor. Between last year when I took the course myself and now when I am a TA/TF, his mental acuity and health has declined significantly. He has essentially no short-term memory, tremors, and can't follow conversations. He rambles, mixes up classes and assignments, and even physically wanders off to look for things (not returning with anything...) in the middle of class.
The students know that something is wrong and often exchange looks when he loses the conversation or rambles.  The faculty certainly does know. His assistant attempted to see someone in the administration for help but they brushed her off, and once the professor found out, he never forgave his assistant and there is a rift between them.
My heart breaks for him. He's had an excellent career and I don't want him to face this kind of humiliation. But at the same time, his condition is so poor that I had to teach the two-hour class today. He must know that something is wrong, too, because he will often make awkward jokes to cover memory lapses.
What can I do? He won't see a doctor. I am afraid of burning bridges with him by confronting him, since that's what happened to his assistant. I don't want to go behind his back to the administration for the same reason. I need his recommendation/reference for my career aspirations. His family is absent. I also worry that any intervention at this stage, in the middle of the semester, will only hurt his students.
Who, if anyone, in a school administration could I speak to about this? Is there someone who handles this sort of thing? Should I? Is it inappropriate for me to insert myself in someone's personal affairs like that?
Update one year later: posted as an answer here.
Let the department head know what you've observed. You can write an anonymous letter if you feel uncomfortable or are worried about burning bridges.

(I've been in this situation, as a student. We - the students in the class - wrote a collective letter to the department head. He was able to arrange extra TA support for the professor for the rest of that semester. He also arranged things so that this professor had other duties in the department going forward, but no more teaching.)