If you are originally in a group, and share a dashboard to it, and then are removed from that group (but still own the dashboard), you can no longer add portlets to it, or edit (with the wrench) portlets under Full Configure. Instead of giving you the option to add a portlet, the Full Configure screen reloads it self when you click the plus icon or click on the wrench.

Steps to duplicate:
Create a dashboard
Share it with a group you are in
Remove yourself from that group
Attempt to edit your dashboard