It's not technically an error. It is a die state; that is -- the die was nice and new at one point, something happened to it (a clash maybe) then the die was not in good shape so someone brushed it down to restore it...and there it is -- a portrait with an unattached nose.
As for extra value...? Hard to say. If someone's collecting such things they might pay a little more for it. You could search ebay for sold listing of similar items. I don't see it having a whole lot of extra value but then there's this three-legged Buffalo nickel with the same issue and it's worth quite a bit. It's all about what the collectors want and are willing to pay.
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