Widget should work like "shopping cart" on e-commerce sites (add to basket style), so when visitor add post to favorites, the list on widget should refresh.
If that is not possible at least "refresh" button would be enough to refresh the favorites widget.
Few other options that would be welcome by many of us I believe.
1. "Remove from favorites" or "X" icon, after each post
2. "Empty" or "trash" icon, to delete whole favorites list
3. "Share/email favorites" Social networks icons and mail
4. "Save favorites list" or "Manage favorites" link to the favorites page
Also some suggestions on design like thumbnails etc.... but those are essential I believe.