July 2013 update: Ancestry.com has recently added a way to filter not only the new DNA Member matches but also the Starred and especially, those with Hints that have a great possibility of having a common ancestor with you.
There is an interesting way to find your cousins who share a direct ancestor and you can see them at a glance. Ancestry.com has conveniently placed a leaf to the right of the column that provides the number of people a person has in their tree. Notice for gdumo30 that they have “No family tree” listed in the second column. It is the next line, G. N. M. that has 7,444 people and are a direct link to one of your ancestors which is notated by a leaf. This is the link you will find the more interesting information with and a possible correspondence connection to. The next person on the list is jk 1304 with 2,248 people and a possible link but not for sure. The last and fourth person, yeaves has 209 people but has locked their tree, as shown with a grey lock, to the public. You will have to ask their permission to see their data.