Before the new season comes, a little look back at the first book / season...
One thing that puzzled me a bit was how the whole parentage of Cersei's children resolved into a big nothing. The first book / season can, in some ways, be seen as a "mystery novel" - the good protagonist, Ned Stark, investigates the murder of the former Hand of the King and discovers the terrible and horrible secret that shakes the foundation of the realm... Cersei's children, the supposedly offspring of King Robert Baratheon, are all born of incest with her brother!!! and Ned realizes it by, essentially, really looking at them: they're all blonde as their true parents and no Baratheon ever sired a non-black haired son.
Ned loses his head, the truth gets out because he informed Stannis and... ABSOLUTELY NOTHING HAPPENS.
The secret was not, well, so secret: it was there in plain sight for all to see, if only one would look. The children are all blonde, once you get told they're Jaimie's it should be crystal clear that it's the actual true, and nobody in the realm gives a damn.
Sure, there are explanations: Stannis broke the news, and he could have passed as self-serving. And even if he was right, he's hated by everyone so no one would want him as king. Then there's Tywin Lannister with all of his power, gold and tendency to go Rain of Castamere on you if you blink an eye the wrong way. But such a big scandal could have really been put away just by the dislike for Stannis and the fear of Tywin?
Just imagine in our real world what even the allegation that William and Henry of England were born of incest between Diana and her brother, with a physical resemblance to back it up, would do. Seems to me that the Lannisters got it very easy, or maybe I'm just underestimating Tywin's power and influence... it's just that there were no real consequences for Cersei and Jaimie - all those who were in arms against them were already so for other reasons, no one in the seven kingdoms said "screw it, Joffrey's a bastard" because of the revelation.