Let's Give the Boy a Hand - S1-E4
Factual error: When Dexter and Doakes are looking at the severed foot wearing a soccer cleat, Dexter states, "The foot was severed between the tarsus and the metatarsus." However, the foot was severed proximal to the tarsus, through the tibia and fibula. The cut was easily too high to be between the tarsus and metatarsus. (00:16:45)
Let's Give the Boy a Hand - S1-E4
Continuity mistake: A photograph of a landfill is shown from when Dexter is a child, but when Dexter goes to visit the location of the former landfill, an old church can be seen in the background. This church likely predates the landfill as evidenced by its Gothic-style architecture. (00:32:00)
Let's Give the Boy a Hand - S1-E4
Continuity mistake: When Doakes is about to be killed by Guerrero, the police save him by shooting Guerrero, giving him a bullet wound on his right shoulder. He is also cuffed on the ground to be arrested. However, when he is pulled up, Guerrero does not have a bullet wound anymore.
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.