"It's not my finest hour" here means that this person made a mistake or did something that he or she is ashamed of doing. For example, if a man was angry at a clerk at a store and berated the man by calling him an idiot. Then, afterwards, a friend who saw him asked what had happened, "it wasn't my finest hour." You could also use it as part of an apology, like it seems to be in your quote. It would convey the idea that there is not excuse for your actions and a sense of contrition. "To be this wrong about someone" is an exaggerated version of the phrase "to be wrong about someone," which means that you misunderstood or misjudged something about this person's character. Example: If you thought that someone was always honest, but then saw them tell a lie, you might say "I was wrong about him." If I'm THIS wrong about someone, then it means you misjudged them even more. "I thought he was a good guy, then I saw him steal money from his own mother. I can't believe I was this wrong about him."