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.
Dexter (2006)
1 stupidity in Goodbye Miami
Starring: James Remar, Michael C. Hall, Jennifer Carpenter, David Zayas
Dirty Harry - S4-E5
Continuity mistake: When Dexter listens to Officer Lundy's tape recording, we hear Lundy say that the Trinity killer's weight is 190 to 200 pounds. When we saw him recording that, he said 200 to 220 pounds.
Dexter: I am a father, a son, a serial killer.
Trivia: Michael C. Hall and Jennifer Carpenter, who play siblings on the show, were actually married in real life, from 2008 - 2011.
Question: Since Harry knew about Dexter's homicidal tendencies, why would he train Dexter on how to kill people who got away with their crimes instead of taking him to a psychologist?
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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.