Okay, the title is a bit misleading for this one. It is not so much the presenter notes that are improved, but rather the way you open/close the presenter notes.
Here is my sample slide, which is not showing the Presenter Notes:
New in PPT 2013 is the addition of a NOTES button on the bottom of the UI.
Click the NOTES button and the Presenter Notes open – no need to fiddle with positioning the cursor and getting the double arrow cursor so you can click and drag to raise up and open the Presenter Notes.
Here is a video of the NOTES button in action
– Troy @ TLC