@Cyan:
He ordered the rape of at least two women, both out of petty spite.
Robb kicks Tywin's ass consistently on the battlefield and Robb basically takes over a good chunk of the Westerlands before Theon's shenanigans began and forced him to head north.
Tywin's campaign in the Riverlands borders on genocidal in scope and conduct. Also letting Gregor Clegane have his way with the countryside makes you a monster by default.
He doesn't care about his children, just what they can bring to his legacy.
The only reason he was viewed as a good Hand was because he got rid of legislation that gave the smallfolk some more legal rights. He doesn't seem to actually view smallfolk as human beings - this is a rather rare view in Westerosi nobility believe it or not.
He demands his children get into loveless but politically advantageous marriages as a way to boost his own prestige, while never remarrying himself.
That "twelve people at dinner" thing? It was more than twelve people - it was dozens at least, most of which were family to the top houses in the North and Riverlands. It also destroyed the foundation of diplomacy in Westeros and put a sociopath in charge of the North.
Ok well find me the quotes that say he was a shitty leader or a shitty commander or a shitty hand. I don't think you will. At best you'll find some quotes about Robb's victories but I'm betting even those are phrased in a way to make it sound like a great accomplishment because he's going against Tywin Lannister.
Today people treat a lot of horrible human beings as heroes. If you didn't get to see so much of Tywin's personal life or if you didn't think the Lannister's were the bad guys you'd have a different view of what he was doing. After all the Tully's kidnapped his son without any real evidence and tried to have him killed. How responsible is Caitlyn for all the lives lost in the riverlands, she must have known such actions would start a war and everything Tywin did was to win that war. Things like this happen in history all the time and depending on whole the victor is that often decides who and what was right/wrong.
Also you're really overselling Robert. The only reason he got the throne was blood. Nowhere in the books is any mentions of political skills, he had the right connections thanks to being fostered by the Aryans and practically being the brother to a Stark who was wed to a Tully. I don't even know what law enforcing skills means but if you're referring to a sense of justice he was glad to see those dead targaryean babies and tried to make more dead Targaryean babies. There's nothing in the books that says he was a Just man.