Continuity mistake: The door to Dexter's apartment opens out toward the walkway. However, in all subsequent episodes the door opens into his apartment.
Other mistake: When Dexter is running Matt Chambers' fingerprint though his computer, he brings up four newspaper articles where the names Matt Brewster and Matt Rasmussen are used. In the final article, the headline reads "Matt Rasmussen of South Boston arrested", but the body of the article uses the name Matt Brewster exclusively. Other than the first few words, the text of the final article is identical to that of the previous one. (00:33:50)
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)
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.