How much detail about mental health issues should one include in "Special Circumstances" section of graduate school applications? This question is inspired by answers and comments to the question "Should a postdoc talk about his depression with his mentor?" on this website.

Suppose that an applicant to a graduate program suffered from some mental health issues during the completion of his previous degrees, and that this situation had a noticeable impact on his academic performance (for example, significantly lower grades or part-time status for one or several semesters).

Most graduate school applications have sections dedicated to providing explanations for such special circumstances, and it is of course strongly recommended that any applicant with unusual drops in academic performance should mention something about this in the special circumstances section. Otherwise, the admission committee will be left to guess what might have happened, which is likely to decrease the odds of being admitted (indeed, it seems a consensus that the more tangible information an admission committee has about an applicant, the more confident they can be about the fact that admitting him will be a sound investment).

Many answers/comments to the question "Should a postdoc talk about his depression with his mentor?" seem to recommend being very careful about revealing details on one's mental health conditions, given that there is still a lot of stigma attached to mental health conditions. However, in the case of PhD applications, not mentioning anything is not an option.

This then leads to the following question: If not making any mention of health issues is not an option (such as in PhD applications), how much details should one go into? To avoid stereotyping associated to any particular disease (such as depression=unreliable, learning disability=not smart) one could limit the description to "health problem", but could this lack of details be seen as suspicious and/or still a situation where the admissions committee will have to do guesswork?
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.