Visible crew/equipment: When they are at the crime scene, you can plainly see the camera and camera man reflected in Special Agent Lundy's sunglasses several times. When it is a close up shot, it is even more obvious.
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.
Dirty Harry - S4-E5
Visible crew/equipment: After the ambulance taking Deb to the hospital drives away, a crew member ducks down in front of a parked car in the background. (00:04:36)
Dirty Harry - S4-E5
Continuity mistake: When Dexter listens to Officer Lundy's tape recording, we hear Lundy say that the Trinity killer's weight is 190 to 200 pounds. When we saw him recording that, he said 200 to 220 pounds.
Dirty Harry - S4-E5
Other mistake: When Lundy is shot and falls to the ground, there is no visible injury even though he is facing the camera. Later, Masuka says he was shot twice, once in the chest and once in the neck. The shooter was facing him. We should have seen the blood.
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.
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)
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.
Slack Tide - S4-E7
Other mistake: When Dexter shreds Laura Moser's file, he actually shreds a file for Estrella Carazo. (00:32:57)
Continuity mistake: When Dexter is packing kill tools for the road he "packs light" and chooses a knife and hammer. However once he's at the hotel room setting up the kill room he unrolls his entire set of tools like he does at all the other murder room scenes.
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)
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)
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.
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.
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.
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?
Continuity mistake: When Lumen stabs Dexter with his knife in the swamp, she hits right above his elbow which he grabs promptly. When the camera angle changes, he's now grabbing his upper arm that's bleeding from a different spot than where he was stabbed.
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: 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.