What is new about the New Covenant?

The first two thoughts that come to my mind are these:

1) Jesus died once for all for sins, there is no longer a need for an atoning sacrifice every year.
2) The new covenant is also open to Gentiles, not just the nation of Israel.

But I think there has to be more. When Jeremiah writes about the new covenant (Jer 31:31-34) he says it will be different than the old one. What was wrong with the old one? The people didn't keep it. "They broke my covenant, though I was a husband to them (v 32)"

So God says he will make a new covenant. He will put his law in our minds and write it on our hearts. He will make us into people that will keep his covenant.

God could have written off the people that didn't keep the first covenant. "Its not my fault," he could say. "Didn't I say 'do this and you will live?'"

But God didn't write off his people, he rewrites the covenant.
(When he opened the new covenant to Gentiles as well as Jews, he didn't write off the Jews. The New Testament talks about Gentiles being included with Israel, it doesn't talk about Gentiles replacing Israel).