Scripted television is not the same thing as real life. That's an obvious statement, but one that needs to be said right up front when presenting a list of fictional characters who don't behave the way people do in the actual world. Still, that doesn't mean characters shouldn't be required to follow a standard set of rules in whichever fictional universe they're in. If you tell me up front that a member of the CSI forensics team has the power of invisibility, that's fine (weird...but whatever), but it has to be consistent. They can't have that ability in one episode and not the next.
Likewise, you can't tell me that a character has a job - one that's incredibly important to them and functions as a plot device in several episodes - and then spend an entire season presenting me with reasons why that character should not be allowed to keep that job...and then let them keep it anyway. That's rude, TV. And I won't stand for it.
Reason For Termination: Negligence Really, from week to week, any employee of the Miami Metro Police Department could have been canned. There wasn't a more grossly incompetent collection of law enforcement officials outside of Reno. (Even Mayberry only had one inept officer.)
The only person who was ever firmly on Dexter's trail was Sergeant Doakes, and - SPOILER ALERT - he was dispatched in Season 2. That left an embarrassing number of seasons where no one questioned why the creepy Forensics guy was always missing at crucial times in an investigation. The core group responsible for Dexter's free reign of vigilantism can be partially excused on account of the higher ups pretty much leaving them to be terrible, without any real consequences.
And who should be dishing out those consequences? Maybe the Deputy friggin' Chief, Tom Matthews. Except, aside from a couple of closed doors, semi-threatening chats with Captain Laguerta about how much her incompetence is ruining his political ambitions, Matthews couldn't seem less interested in the entire police department. Does nobody higher up than him really care about how his lack of involvement? Really? Do we just need to fire the entire city of Miami?? Also, remember that Tom Matthews has known Dexter for nearly as long as his sister, Deb. And he's still unable to connect the dots to everyone's favorite sociopath.