A probate court in Pennsylvania is determining whether the heir to the DuPont fortune had the capacity to execute a valid will. http://www.philly.com/philly/news/pennsylvania/123980894.html
In Minnesota, testamentary capacity means that the person executing the will knows the "nature, situation, and extent" of their property, the claims of others on their estate, and be "able to hold theses things in their mind" long enough to make a rational decision in distributing their assets. Check out the case of In re Estate of Torgersen, 711 N.W.2d 545, for more explanation. You don't have to be a financial genius to have capacity, just need to meet those three minimum requirements.
If you are setting up your estate plan and are thinking about disinheriting someone, a good idea is to request that your attorney ask you questions to demonstrate your capacity and record that conversation. That way, if anyone questions whether you had capacity when you made the will, there will be evidence showing that you did. If you're setting up a plan that disinherits someone, speak with a licensed attorney in your area about preventing questions of capacity.