While I agree that the the characters' morality in this show is grayer than usual, which I find refreshing, I think the "badder" characters have a good amount of plot armor. Lysa is crazy enough to not grant assistance to her sister, but not crazy enough to simply deny Tyrion his trial by combat. Jaime Lannister brazenly attacks Ned Stark in King's Landing and the consequences of his actions are pretty much nothing. Later, he escapes Robb's custody due to a combination of lucky breaks and the most incompetent prisoner management in Westeros. And of course in the process of his extremely lucky escape, by killing Karstark's son, kicks off events that lead to Robb losing the support of Karstark. Joffrey screws up Ned being sent to the wall and provokes the North, and yet in the subsequent war of five kings the Lannisters' enemies practically trip over eachother's swords. Littlefinger makes an incredibly transparent scheme to blame Tyrion for the assassination attempt on Bran, in front of Varys no less, and it somehow works. Arya Stark wastes her three hits from Mr. Badass Assassin on Lannister nobodies instead of anyone of consequence. The Ironborn decide to raid the frigid north instead of the wealthy Lannister lands, despite the fact that they are both equally distracted by the war. Theon Greyjoy somehow takes Winterfell with a crew of third-rate sailors. I don't care how undermanned your castle is, that is an act of plot. The result of trials by combat are extremely predicable: The "bad" party will win, no exceptions. None of these on its own proves much, but I think together they represent a trend.
Of course there are exceptions, but they have little effect on the plot. Arya, Sansa, Bran and Rickton survive, but while their adventures are fun to watch, they ultimately mean little to the greater conflict. Robb wins early victory, but doesn't end up killing anybody on the Lannister side who is actually important, none of the Lannister's enemies are able to exploit his victories, and he ends up getting killed off. Joffrey is assasinated, but at that point he was a liability to the Lannisters. Drogo dies, but only after it looks like he could be a threat to the Lannisters.
It seems that the "gooder" portion of the characters certainly bare the full brunt of realism while the "badder" characters are given many lucky breaks.
Don't get me wrong. I like Game of Thrones. But I do not think it is "realistic" fantasy, despite what many fans claim. I think people confuse "dark and gritty" with "realistic".