Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Revealing mistake: Sgt. Batista shows Dexter a dismembered leg with the hip bone protruding. The hip bone looks ridiculously fake, with plastic seams and the pin used to attach it to anatomy models visible. (00:26:05)
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.