One approach is to configure your social hub to auto-publish each new post. Then, when viewing your social hub (and only when logged in as a TwineSocial user with moderation privileges) you can remove individual posts and mute users. Simply mouse over the offending post and click the "Hide" button or the "Mute Person" button:
When you added your data feeds, you had the choice of sending all social posts from this source to a "Drafts" folder, where it must be approved before being published to your social hub. To access this content, navigate to the "Drafts" section of your social hub admin in TwineSocial:
Mouse-over each post and click "Approve" to post this item to your social hub. Convenient dropdowns above your hub let you drill on on unapproved content by data feed, or to see items that have been moderated out.