Other mistake: When Dexter is running Matt Chambers' fingerprint though his computer, he brings up four newspaper articles where the names Matt Brewster and Matt Rasmussen are used. In the final article, the headline reads "Matt Rasmussen of South Boston arrested", but the body of the article uses the name Matt Brewster exclusively. Other than the first few words, the text of the final article is identical to that of the previous one. (00:33:50)
Continuity mistake: When Dexter and Deb are celebrating her promotion, just before they toast and you look at them from the side Deb has her hands free, when the camera changes she has a crab leg in her hand, and when the camera changes again her hands are empty once more. (00:46:45)
Answer: No, Harry is not the real father. While he did have an affair with Dexter's biological mother (Laura Moser), this was when she was his C.I. Dexter was already born at that point.