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)
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: In the scene where Rudy's body is found by the police, you can see Rudy breathing and his pulse in his neck. (00:51:05)
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)
Revealing mistake: The dead body appears to be moving its eyes. (00:10:05)
Revealing mistake: When Dexter is retrieving a blood sample after cutting Benny Gomez's cheek, there is no blood in the dropper and he puts no blood on the actual slide. (00:49:50)
Revealing mistake: When Rita confronts Dexter about his accident being more than minor Rita turns the buggy with the baby in around to leave and it is clear the baby is fake. (00:38:20)
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.
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: When Dexter is fighting Liddy, in the van after kidnapping Dexter, the knife is a rubber fake knife. (00:38:15)
Revealing mistake: The actor portraying a dead body noticeably moves her left leg while being turned over by Angel, Dexter and Masuko. (00:06:33)
Sunshine and Frosty Swirl - S7-E2
Revealing mistake: After Isaak Sirko killed Tony Rush by sticking a screwdriver in his eye, Rush almost instantly drops dead on the floor. When Sirko's assistant, Jurg, wipes the screw driver for finger prints, you can still see a pulse at the base of Tony's throat. (00:54:05)
Revealing mistake: When Dexter enters his apartment and finds Zach dead in the chair, you can see Zach's chest moving, showing he's breathing. (00:49:45)
Remember the Monsters? - S8-E12
Revealing mistake: In the flashback scenes when Dexter and Deb are shown holding baby Harrison in the newborn room, you can tell they are just holding a dummy in the wide shots because the baby never moves a muscle.
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.