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)
Continuity mistake: Episode 3 begins with Dexter at the beach during a funeral. He is wearing a pair of stylish sunglasses. At the start of episode 4, Sgt Doakes is investigating a crime scene at the beach. He is wearing the same pair of sunglasses. Given the tense relationship between the two characters, it is unlikely they would share accessories.
Revealing mistake: When Valerie's dead body is on the table after being brought up from the ocen by the ice truck killer her nipples are hard. If she was dead her nipples would not have any reaction to the cold.
Revealing mistake: Sgt. Batista shows Dexter a dismembered leg with the hip bone protruding. The hip bone looks ridiculously fake, with plastic seams and the pin used to attach it to anatomy models visible. (00:26:05)
Seeing Red - S1-E10
Continuity mistake: When Angel is at the bar, the girl he is talking to has a drink held up by her face when viewed from behind. In every shot from in front, the drink is on the table.
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.