How to get rid of empty blocks on the dashboard?
I think this is a long-standing issue with dashboard blocks. See the discussion, and several patches, here: https://drupal.org/node/936798

I haven't tried any of these patches myself.

If you just want to get rid of the error, I believe you can delete inactive blocks in the database directly, as described here: https://drupal.org/node/1202500

The gist is that you look for and remove blocks in the block table where region = dashboard_inactive