Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Other mistake: When Dexter is running Matt Chambers' fingerprint though his computer, he brings up four newspaper articles where the names Matt Brewster and Matt Rasmussen are used. In the final article, the headline reads "Matt Rasmussen of South Boston arrested", but the body of the article uses the name Matt Brewster exclusively. Other than the first few words, the text of the final article is identical to that of the previous one. (00:33:50)
Continuity mistake: When Dexter is killing Stan Beaudry, the drop of Beaudry's blood encompasses the width of the blood slide when the two pieces of the slide are pressed together, but then goes to being roughly half the size when the shot changes.
Dirty Harry - S4-E5
Revealing mistake: After the intro at the start, it cuts to Dexter passing the fire engine, and the next long shot with a firefighter lifting the yellow tarp is a flipped shot; note the backwards licence plate, sign, etc.
Continuity mistake: In Paris, when Dexter grabs the knife off the table in the close-up, he's wearing the black glove on his right hand, but it cuts to the wide shot and both of Dexter's hands are bare; then in the next shot the black gloves reappear. It's rather odd that the actor was even filmed without wearing his gloves in the wide shot.
Hungry Man - S4-E9
Visible crew/equipment: When Dexter rings Arthur Mitchell's doorbell Sally opens the door, and in the next shot facing Dexter, the reflections of equipment and crew, such as one crew member standing on a ladder (appears orange), are visible on the door's glass at the left side of the screen. (00:18:35)
Everything Is Illuminated - S5-E6
Continuity mistake: Lumen has a dark "H" shaped scratch on her right shoulder. A few minutes later, its turned 90°, like a sideways "H," and it is very faint. (00:22:05 - 00:32:35)
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.