Visible crew/equipment: When Dexter is searching the empty house, you can see a crew member with his sunglasses on outside the window. (00:45:49)
Are You...? - S7-E1
Factual error: During the walk-through of the crime scene, there is a small remnant of plastic sheeting between Travis' toes. Given the entire church was consumed by flames, or more importantly, the body and foot from which the plastic is pulled are badly burnt, it's highly improbable that the plastic sheeting would still be present. At least not in the form that is shown, but rather more like a globe of melted plastic on or into the body or table. Similarly, the feet wouldn't be 'wet' or glossy with blood. (00:15:22)
Continuity mistake: When Hannah calls Dexter at the bus crime scene, Dexter answers the phone normally but then in the next cut, the phone is upside down. (00:23:25)
Revealing mistake: When Dexter stomps on Barry's kidney, you can see his foot doesn't even make contact with Barry's body.
Revealing mistake: After Doakes remarks that the dead body of Eva is a message, you can see the actress' neck throbbing around where the trail of blood is. (00:06:49)
Continuity mistake: When Dexter leaves on his boat there are fishing poles behind his seat, but when he turns back around and you see him going away on the boat they have gone.
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)
Shrink Wrap - S1-E8
Visible crew/equipment: When Dexter is picking up the fruit dropped by the man carrying groceries, the cameraman is reflected on the side of the car. (00:17:30)
Our Father - S3-E1
Continuity mistake: When Dexter and Vince are next to the dead girl, in the side shot, the tied string from her top is visible on her back and her hair is to the side. But in the overhead shot of her, her hair is covering the tied string and spread more over her back.
Just Let Go - S6-E6
Factual error: When Dexter is looking at Leo Hernandez's criminal history, it shows Leo's social security number. However, it's a 10-digit number instead of a 9-digit number.
Do You Take Dexter Morgan? - S3-E12
Character mistake: The petition for dissolution of marriage was filed on Jan 6, 1990 which is less than 5 months of marriage. However, the duration of the marriage says it's been 6 months.
Continuity mistake: Deborah walks out with the yellow shirted man in front of her. Next shot after Quin leaves, the same man re-exits the room. (00:14:00)
Just Let Go - S6-E6
Continuity mistake: When Travis meets his sister at the school she works at, a chalk board with nothing on it can be seen behind Travis. A couple of shots later and there is a piece of paper attached to the chalk board. (00:30:35)
Continuity mistake: When Dexter and Masuka are discussing wanting to go home Dexter throws a can toward the bin and misses, landing by Masuka's chair. In the next shot as Masuka leans down to pick it up it is closer to the bin. (00:39:30)
Our Father - S3-E1
Other mistake: When Debra is talking about her new haircut, she states that she has changed her hair "for the first time since she was 8." However in various flashbacks throughout the show she has drastically different hairstyles from her 'usual'.
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)
Revealing mistake: When Deb is texting "Looks like it" to Anton, the buttons she presses on the keypad do not correlate with the message itself and the phone doesn't show any auto-correct feature being utilized, indicating that the text message was added in post production.
Other mistake: An extra is walking in the background with a measurement wheel while Debra is talking with Lundy outside of the warehouse. The character is hovering the wheel over the ground and not actually using it for its intended purpose. (00:17:10)
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.
Continuity mistake: Deb moves in with Dexter to his apartment in a 2nd bedroom during season 2 following the ice killer's kidnapping and attempt on her life. But in Season 5 when they try to share this apartment again, it's only 1 bedroom now?
Answer: Two reasons. First, as a cop he knows that there are lots of murderers walking around free due to flaws in the system so he uses Dexter's "urges" to right the wrongs in the system by taking out people who have no right to walk around free. Secondly, by taking him to a psychologist he runs the risk of having him committed and he doesn't want that for obvious reasons, so he figures it is best to channel his urges to what he considers a greater good.
The_Iceman
In addition to the earlier answer, in the last season (8th) of the show, we are introduced to Dr. Vogel, whom Harry had been discussing the situation with Dexter as well, and it is shown on-camera that Harry describes what Dexter has done (killing)... So, technically he did consult a psychologist/psychiatrist, just not having Dexter and her actually meet. But Dr. Vogel was aware of whom it was and how to intercede.