Remember the Monsters? - S8-E12
Plot hole: In order to elude Elway at the airport, Dexter fills a backpack with random items and leaves it unattended under a seat, and then tells a desk clerk that he saw Elway deliberately put the backpack there and walk away, which leads to security detaining Elway and the airport being evacuated. Airports have security cameras everywhere, so security would have reviewed the footage and seen Dexter was the one who placed the bag there. They then would have gone through all security footage since he entered the airport in order to deduce his identity and then located and arrested him.
Remember the Monsters? - S8-E12
Plot hole: A couple episodes prior, Deputy Marshal Clayton stated that he shared Hannah's picture everywhere after receiving a tip that she may be in Miami. In the same episode, Hannah was spotted at a hospital and Clayton was called in about it. This should have only increased public awareness concerning her, but at the beginning of this episode, she somehow made it through airport security and all the way to her gate before spotting Elway and hiding from him in the ladies room.
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.