Trivia: (POSSIBLE SPOILER) When Masuka brings up the list of doctors authorized to get the M99, Dexter removes his alias note that Dexter's fake alias (used to get the M99 tranquilizer) is Dr. Patrick Bateman. Patrick Bateman is the lead character of "American Psycho". This was most likely an intentional "easter egg" of sorts within the show.
Trivia: Some notable differences between season 1 and "Darkly Dreaming Dexter" - the first novel in the series of books that the show is based on - are that Deb and LaGuerta both discover Dexter's secret by the end, which doesn't occur in the show until seasons 6 and 7, respectively. LaGuerta is also killed by Brian, a.k.a. the Ice Truck Killer, whose true identity isn't revealed until the last chapter, and he is also referred to as the Tamiami Slasher. He also escapes at the end of the novel.
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.