Continuity mistake: Dexter goes to the morgue to see the body of his father. When he first sees the body, he bends down, and the clock behind him reads 4:11. A moment later when he stands back up the clock is at 4:17. A couple of minutes later the clock is at 4:01.
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.
Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Shrink Wrap - S1-E8
Continuity mistake: The Ice-Truck Killer is responding to Dexter's Craigslist submission. The reply-to e-mail address is frozenbarbie@hotmail.web, but when in the new window that popped up when the ITK hit "Reply" the address is frozenbarbie@hotmail.com.
Shrink Wrap - S1-E8
Continuity mistake: When Doakes asks Deb "what took her so long" arriving at the first crime scene, Masuka is stood next to him. However, over the course of the conversation Masuka is seen in the background talking to another group inside the house, and in the next shot he is standing back next to Doakes. At the end of the conversation he walks over to the group inside the house. (00:05:30 - 00:06:00)
Continuity mistake: When Shanda is sat on Debra's desk, her handbag keeps moving from on her lap to at her side between shots.
Continuity mistake: When Dexter and Deb are celebrating her promotion, just before they toast and you look at them from the side Deb has her hands free, when the camera changes she has a crab leg in her hand, and when the camera changes again her hands are empty once more. (00:46:45)
Continuity mistake: When Rita is talking to Bob outside the house, she is carrying a box. A piece of tinsel keeps moving from hanging over the edge of the box, to being tucked inside.
Continuity mistake: When Rudy has Debra in a headlock on the yacht, his left hand continuously moves between shots from on her head to gesturing in the air.
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)
Seeing Red - S1-E10
Continuity mistake: When Angel is at the bar, the girl he is talking to has a drink held up by her face when viewed from behind. In every shot from in front, the drink is on the table.
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.