I think we are forgetting something in Jaime's arc, when Jaime killed the mad king, he was a teenager. We also can infer that at one point he wanted to be an honorable knight. Brienne represents to him what he wanted to be at one time. I think however that the course of his life was significantly altered after that one incident that labelled him the Kingslayer. Here we have this teenager who does the right thing, he breaks his oath to save a city ( and not kill his father) and the entire world turns against him and mocks him. At that point he probably just gave up on being honorable. Ned Stark walks in and there is judgement in his eyes, and to a teenage Jaime, yes killing Aerys was probably justice for the Stark brothers who he saw burned in front of his eyes. He was a teenager, at that point all of his bad deeds had yet to occur.
However Jaime shouldn't have cared what Ned thought, but he probably looked up to Ned as a paragon of honor and figured if Ned judged him then the whole world would too. So he says nothing and instead goes down the twisted path he did.
1) Twincest : in a world where the Targaryens are known for sibling marriage I am not going to put too much stock in this. Unfortunately he was/is inlove with his sister
2) Pushing Bran out the window: this is probably the only thing truly I hold him accountable for..Robert would have surely killed Myrcella/Tommen if he found out the truth. I'm not adding Joffrey because well....Joffrey needs to die
3) Killing his cousin : This is Westeros, he was in jail and he saw and opportunity to escape and he took it, it wasn't a nice thing to do but I see why he did it.
Jaime is changing and evolving, he may be on a path to redemption or he may just revert back to his former self.