It is wrong. It should read either The Smit hs (which is plural and refers to the family members as a group) or The Smith s' (which is plural possessive and refers to the family home).
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the Smith's - home is where our story beganWhy the dash? It makes it unclear which of two things you're trying to say -- The Smiths as a title, or The Smiths' home as the subject of a complete sentence?