Slack Tide - S4-E7
Other mistake: When Dexter shreds Laura Moser's file, he actually shreds a file for Estrella Carazo. (00:32:57)
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.
Other mistake: An extra is walking in the background with a measurement wheel while Debra is talking with Lundy outside of the warehouse. The character is hovering the wheel over the ground and not actually using it for its intended purpose. (00:17:10)
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.
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.
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.