Much ink has been spilt over possible Jewish connections and stereotypes in the Potter-verse (personally I saw neither when I read, but I was mainly reading for the characters and narrative). One aspect I have not seen, though, is Rowling's perspective on what it means that Harry is "chosen".
There is debate about whether Jews should continue referring to ourselves as "the chosen people", both within and without the Jewish community. Some feel there is an implication of racism or superiority in the name, as we were chosen because we are somehow better or have special privileges because of that choice. Others see the name as a historical artifact, like calling Japan the "land of the rising sun", that has little meaning today. But what would Harry say?
One of the reoccurring themes of the later books and movies (spoiler alert!) is that Harry only became the "chosen one" when Voldemort chose him. Harry's classmate Neville is presented as another candidate that fills the prophesy as well as Harry (and to many would have made a better savior as well), but because Voldemort pursued the Potter family, Harry became chosen. It was the act of attacking, in fact, that created the situation that gave the "chosen one" his "powers".
This is supported by the arc of the books. Harry is never the smartest or strongest or best student. He barely has any defining heroic characteristics at all, except maybe for courage and leadership. And even those arguably are a result of his choosing, not something innate, and anyone that survived (by luck and support of his mentor) the same type of early adventures he did would develop those traits.
So what does that say about the Jews? This week's Edible Torah includes a discussion question about a verse that reminds us we were not the largest nation, but the smallest. The implication, reinforced by other midrash, is that we were the nation willing to accept what God offered and required. One could even argue that we needed the protection, so signing up seemed like a good deal. If there were any traits the Jews possessed they were faith and loyalty, and who's to say any nation that had received so much from God would not have developed the same traits to the same degree?
We became chosen because God chose us. Nothing more, nothing less.