In a story where no one's perfect, including the noblest character in the show(besides maybe Sam) in Jon. He executed a young boy. It's hard to hate Jaime. I think he generally has a good heart, he's just weak and was bred in a screwed up family. Family is all he knows, he was preached undying loyalty all his life, so naturally he's overly loyal.
Even if I don't agree with all his motives, I can at least understand where he's coming from logically, which I can't say about all the characters in the show. Also, he still has room to majorly redeem himself even more if he takes out Cersei eventually.