Our Father - S3-E1
Revealing mistake: During the crime scene investigation where Dexter, Masuka, Debra, and Angel arrive, a production mistake is visible. The victim, who is supposed to be dead, can be seen breathing - the back moves slightly while the camera is still on the body. (00:52:45)
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)
That Night, A Forest Grew - S2-E7
Continuity mistake: When Deb meets Lila, Lila is at the fridge and puts her arm over her breast - she isn't wearing the 'engagement' ring. However when she returns to Dexter's room it's on her finger.
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.
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
Factual error: When Dexter and Doakes are looking at the severed foot wearing a soccer cleat, Dexter states, "The foot was severed between the tarsus and the metatarsus." However, the foot was severed proximal to the tarsus, through the tibia and fibula. The cut was easily too high to be between the tarsus and metatarsus. (00:16:45)
Do You See What I See? - S7-E11
Continuity mistake: Deb's daily drive is an E46 '03-'06 BMW 3 series. In this episode she is in a car accident and when Dexter shows up at the salvage yard to check the vehicle he is led to an E36 '95-'99 3 series. (00:18:45 - 00:36:25)
Factual error: When Dexter is punching Olivia's father in his left side, he says "That's your liver." Only the liver is on the right side. For a serial killer who routinely dismembers bodies, Dexter should know which side the liver is on. (00:42:50)
Do You Take Dexter Morgan? - S3-E12
Other mistake: The marriage certificate for Rita's first marriage shows her date of birth as 04-19-1989 and Dexter states she married at 16. The marriage date is 08-16-1989, when she would have been 4 months old. She also would only be 17 at the start of the series (2006) if she was born in 1989. (00:13:45)
Factual error: When Dexter is in the hospital as a child, the doctor says that Dexter has a very rare blood type, AB negative. Although it's very rare, the people with AB- can receive donor blood with A-, B-, AB- and 0-. AB- is a very good blood-type when you need to receive blood. While it is true that hospitals normally have to use AB- because of the complexity of other proteins (and to prevent adverse reactions), in case of an emergency, like Dexter's, and a shortage, a hospital will use a blood type close enough to not likely cause a reaction. In this situation, the hospital would give Dexter O-, B-, or A- instead as blood loss would normally kill a patient long before a suitable donor could be located, called in, admitted to the hospital, and have the transfusion set up. (00:31:00 - 00:32:00)
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.
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: Near the beginning of episode 3, season 7, Dexter is attempting to take a mouth swab of a criminal in the interview room. When he first sits to request a swab from the man he is shown putting on forensic gloves. When the camera pans to him a second time to attempt taking a swab he no longer has forensic gloves on. As the man resists opening his mouth for a swab check Dexter is wearing forensics gloves again.
Are You...? - S7-E1
Continuity mistake: When Dexter started removing the plastic off Travis' body, his small knife was stabbed into the chest, but during that, the sword was already stabbed into the chest, not the knife, and then again, he removed the knife from the body, and then stabbed him with the sword. (00:12:05)
Factual error: In The Beginning while Dexter is on his boat in Miami, you suddenly see mountains in the background, of which there are none in Miami. Also the palms are too high, indicating they are from California. And the worst setting mistake is the Florida tags in front of the cars. Only commercial vehicles have front tags.
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.
See-Through - S2-E4
Visible crew/equipment: When the wife of one of the victims invites Angel in, the silhouette of a camera man is reflected in the door when she closes it.
Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Our Father - S3-E1
Continuity mistake: When Dexter gets out of the car and talks to his sister, the strap on the camera keeps flipping back and forth. (00:52:45)
See-Through - S2-E4
Visible crew/equipment: As the camera pans to Dexter just before he jumps over the fence at the police station, the shadow of a boom mike is visible on the white wall.
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.