Fred Thompson told her that she was fired because she was too passionate about being a prosecutor, that she was too much into advocacy. As a prosecutor myself, there's something to that, but for this t.v. show, that's an incredibily lame and stupid reason.
On tonight's show the primary Defendant was not guilty of murder (his "best friend from the hood" was), and she kept harping on his being innocent to McCoy and Thompson, and whining that no one listens to her. She even went so far as to confront the Defendant, without his lawyer present, and try to convince him to turn his friend in. That little stunt would get a lawyer in serious trouble (but they completely ignored that aspect on the show).
From what you say they did something they always do on TV when they get lazy--for ONE episode they play up an aspect of the character, then the payoff relies on us thinking this was the character's usual mode of behavior. For example, say there's a movie about pilots, and for one episode they keep harping on the character for "always being a daredevil", except he's never been particularly reckless...until THIS episode. Sounds like what happened here.