Continuity mistake: When Dexter is killing Stan Beaudry, the drop of Beaudry's blood encompasses the width of the blood slide when the two pieces of the slide are pressed together, but then goes to being roughly half the size when the shot changes.
Continuity mistake: Arthur and Dexter make a u-turn to avoid a DNA checkpoint. The view from outside the van shows no oncoming traffic, but the view from inside the van shows several cars waiting for them to complete the u-turn. (00:53:20)
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.