The main innovation is the proof of the Wilber-1 bound. As opposed to the somewhat hairy proof in Wilber's paper and in our paper's appendix, I show Wilber-1 by arguing about the problem geometry and maintaining partial sums (forget trees!). Hopefully this gives a more intuitive proof. In any case, it shows the students something very important in its own right.
If you read these notes, I am interested in anything you have to say, including things you didn't understand, or suggestions for clarifications.