There's no way to show all comments from Facebook either on the front-end or admin area. It's something we're investigating, but it basically means we have to periodically fetch all comments from Facebook and store them in your database. Facebook, unfortunately, doesn't have a way that we can simply say "Get all comments for domain xyz.com". So, to do what you're looking for will take a lot of work.
It is something we want to implement as it makes things nicer in quite a few ways, like allowing for Latest Comments modules and other type features. Until then though, to see all the comments, you can use the moderator tool you mention as the admin.
Hope that explains, even if it's not the answer you were looking for,
Alex
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