How much detail about mental health issues should one include in "Special Circumstances" section of graduate school applications?
You do not have to disclose your personal health history (including mental health) to graduate schools  when you are applying -- and even while you are enrolled. 

There are occasions where you may want to. For example, if there is a semester in your undergraduate record where you did particularly poorly because of (mental) health issues, you may want to note this is in your diversity statement or special circumstances portion. However, you can be as vague as you want -- saying "In the fall of my junior year, my health declined which led to poor performance in a number of my classes. I recovered the next semester and you can see that my senior year grades were all of the highest rank."

If you have faculty writing letters of recommendation for you who know about this incident, you may want to tell them: 1) if you want them to mention it or not; 2) what language to use ("she became depressed following a family death" vs. "She struggled with the additional family issues following the death of her mother" vs. "There was a family crisis that took her away from school that semester", etc.etc.).

Otherwise, your (mental) health record  is your personal medical information. The professors in your department do not need to know it -- any more than they would need to know that you had HIV or were on dialysis. If you need accommodation (such as taking Wed and Fri off for dialysis, or for therapy) you may want to disclose that to some people but you should feel free to compartmentalize the information to certain people and to not disclose everything about your condition.

For example, it is entirely appropriate to tell just your advisor, department chair or director of graduate studies -- or external to the department: your university ombudsperson, disability services officers, or associate provost or dean -- some of the details of your condition and what accommodations you need to be a successful scholar, but ask that the information not be shared with faculty members in the department.  But again, this is your choice.