Factual error: In the newspaper article from the Trinity killers past - the report states that someone called 911 and dispatch gave them instructions. The death occurred in 1959. The first 911 call was made in 1968. (00:39:24)
Character mistake: In this episode, as well as 1-2 others, Dexter holds his slide phone upside down (only in the edits/cuts where he wasn't shown answering the phone). When the phone is slid open, the front cover goes above/higher than the backside of the phone. And a few instances I've seen, the side closest to his face 'lower' than the outside/backside of the slide phone, strongly suggesting the phone was held upside down.
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.