They keep talking about "One for All" in an ominous sort of way. Not really dark, but they keeping hinting at something about it, I just can't put my finger on it. It's as if after hearing the story the person who uses the quirk changes a bit, maybe mentally? I feel like something bad happened to the original user, Shimura.
I honestly thought he was going to end up as a villain, I still sort of do. I feel like his character might break a little bit when Midoriya starts to fight him evenly without trouble, or Hell even beats him. Or he could gradually accept it and grow stronger from that, but his character is clearly on the edge. His goal is literally becoming the strongest hero. It doesn't really contain a good sense of morals for what a hero stands for... Not that everyone needs to be a knight in shining armor, but with that he can easily be manipulated by power.
Imagine if the Villains offered to give Byakugou more quirks so he can become more powerful in exchange for his loyalty? I see a possibility where Midoriya and Todoroki begin to excel at a faster rate he does, and he begins to question himself.