Continuity mistake: Dexter kills Jimenez with a chainsaw and is wearing an apron. But he gets blood all over his shirt. He leaves in a hurry after getting a call from Rita about her door being unlocked and him having the only other key. When he shows up, there is no blood on the same shirt he was wearing.
Continuity mistake: When Dexter wakes up in front of Rita's house, he has a sweat patch on his shirt. When he gets into his car a minute later, it's gone.
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.