Banks absolutely make mistakes in the favor of the client all the time.
In general, banks want to get it right. If they want to make more money, they can always change the terms. Not saying that all banks are snow white lilies, but they generally want to have everything accurate to the rules. The way they win is by helping to write the rules.
The little town banks maybe. Frankly, the national one I think try to get away with as much as they can. And their bonus system is probably to blame: "by the time this is discovered, I'll be gone with my bonus."
Do they ever mistake to give people free money (at such scale?) I bet the stealing happens a lot more often.