Factual error: In the newspaper article from the Trinity killers past - the report states that someone called 911 and dispatch gave them instructions. The death occurred in 1959. The first 911 call was made in 1968. (00:39:24)
Remember the Monsters? - S8-E12
Plot hole: In order to elude Elway at the airport, Dexter fills a backpack with random items and leaves it unattended under a seat, and then tells a desk clerk that he saw Elway deliberately put the backpack there and walk away, which leads to security detaining Elway and the airport being evacuated. Airports have security cameras everywhere, so security would have reviewed the footage and seen Dexter was the one who placed the bag there. They then would have gone through all security footage since he entered the airport in order to deduce his identity and then located and arrested him.
Remember the Monsters? - S8-E12
Plot hole: A couple episodes prior, Deputy Marshal Clayton stated that he shared Hannah's picture everywhere after receiving a tip that she may be in Miami. In the same episode, Hannah was spotted at a hospital and Clayton was called in about it. This should have only increased public awareness concerning her, but at the beginning of this episode, she somehow made it through airport security and all the way to her gate before spotting Elway and hiding from him in the ladies room.
Are You...? - S7-E1
Plot hole: It's out of character and against his code for Dexter to kill Viktor at the airport. Airports have security cameras everywhere (you can see one on the ceiling when he is wheeling Viktor into the unclaimed baggage storage), and using the unclaimed baggage storage as the kill room is equally unwise, because any airport employee could walk in at anytime and catch him red-handed. Dexter was caught murdering Travis Marshall by Deb just hours before, so if anything, he should be even more cautious.
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)
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?
Do You Take Dexter Morgan? - S3-E12
Other mistake: Debra is checking her email for the traffic cam photo of George King. The sender is labeled "Miami Metro Robbery Div." and the subject is "Photo of George King." However, after opening the email, the send is then a malformed email address of Det.Robertson.Robbery|MiamiMetroPolice.web with a recipient address of Debra.Morgan.Homicide|MiamiMetroPolice.wed (wed, not web), with a subject of "B. O. L. O. Match - George King." (00:26:38)
Other mistake: Lumen agrees to meet her former fiancé Owen at noon. When they meet up, the sun setting in the background indicates that it's evening. (00:16:12 - 00:23:39)
Other mistake: There's no way Arthur could have known Scott was 10 years old. In fact, it's highly likely he would not have known any of the boys he killed were 10 years old.
The Getaway - S4-E12
Other mistake: The tub Rita was found in was full of water, to the rim. Volume displacement dictates that when Arthur got out of the tub the water level would have dropped to well below the tub's rim.
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.