For security and auditing purposes, it would be helpful to be notified when a user resets her/his pw via the password reset. This should include the users name/username and method (person, school, etc.) but not the password.
This email should be triggered when a reset occurs. I am undecided, but I am not sure if it should also be sent by the initial request as well. There may be a case for both but I definitely would like notification of an actual reset.
Including the user's role within Genesis may be helpful as well. i.e. email notes if the user is a student, faculty, staff, admin, etc. This would help raise flags for faculty and admin changes. ex: if someone was trying to break in and change a grade. I don't think that would be an NTS problem, but I can see it being helpful for undergrad etc where the students are not all ministry minded.