Stupidity: Dexter's decision not to kill Trinity when he had the chance eventually led to Rita's death, a mistake Dexter told Deb he would never make again. However, at the end of this episode, he decides to spare Oliver Saxon so Deb can arrest him. Dexter doesn't stay to ensure that Deb successfully has Saxon in custody, which leads to Saxon escaping his shackles with the unwitting help of Deputy Marshal Clayton, and shooting Deb before leaving the scene. Dexter therefore does make the same mistake again.
Stupidity: After Dexter tells Hannah that the U.S. Marshals have distributed her picture everywhere, she questions how she will be able to flee Miami for Argentina. Dexter reasons he and Harrison can leave with her because the authorities won't be looking for a woman traveling with her "husband and child." It doesn't matter who she is or isn't traveling with. If the authorities have shared her picture, she's going to be flagged when she goes through security at the airport, which Dexter should certainly know. This is made all the more egregious when she takes Harrison to the hospital later in the episode and is ID'd by the receptionist.
Stupidity: Hannah spends the entirety of season 8 as a fugitive in hiding, but never thinks to make herself less conspicuous, such as dyeing or cutting her hair, or wearing disguises when she goes out in public.
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.