I've read the documentation on "mark private", and it appears to make sense, albeit the name of the control is counterintuitive. I.e., "If I want to share it, I have to mark it private first" is... just weird :)
If I may be so bold, I would suggest the following two options:
Visibility: () Myself (x) Admins, () and Hiring Manager, () and other Interviewers, () Whole Company (i.e., the default - Admins - is the current behaviour)
Additionally: [ List of Additional People ]
The "Additionally" field is always there; no need to adjust the visibility option to add additional shares.
Also, I think the option to "collapse" a note - requiring a click to see it - isn't useful enough to link it to the visibility option. Why not just have all notes collapsed, and there's an link to expand individual notes, or all notes.
Closing the case would then either switch the visibility to "Admins" or "Note Writer (Myself)" at the Admin's option. I think "Admins" is just fine, but "Note Writer" would be appropriate if the candidate may potentially be a JobScore admin.