At the start of the series, Box was pre-occupied with retiring and so he was uninterested in spending a long time investigating every possible angle to Andrea's murder when he had, due to the really fuckin strong evidence against him, a suspect who's only problem is that he didn't really seem like a murderer. There were some other inconsistencies, but with his retirement coming up, and a lifelong career focus of getting convictions for his cases, he went with the path of least resistance and focused on Naz entirely.
Then he actually retires, and he finds himself with a lot more time on his hands to think. Being as it was his last case, he dwells on the things that didn't feel right about it, and the fact Stone needled him about him knowing it wasn't the right man for the crime probably contributed. So he decided to look into it a bit more, maybe just for his peace of mind, exploring some of the other possibilities ie looking at Andrea's movements earlier in the night before she met Naz. This led him on to find what at the end of the series looks like a more likely culprit of Andrea's murder than Naz. His cop friends are bemused as to why he is still hanging around the office when he has officially retired, but he doesn't know what else to do, and this is bugging him now.
He decides to take this evidence to the prosecution, who reject it, and then after Naz is acquitted, he decides to help apprehend this person who is now looking likely to have killed Andrea. So he gets some small measure of personal redemption for himself, but in fact he did nothing at all when it was crucial and was almost responsible for a man nobody can prove is guilty spending the rest of his life in jail, and he likely has been before in his life, and doesn't even know it. He just trundles along, not solving half as much as he hopes he does, and ruining countless people's lives in the process, whether he has the right culprit or not, a 'subtle beast'.
That's basically Box's character arc. Pretty clear cut to me.
