Me too -- mid-2013 MBA 13. Damn annoying!
EDIT: And as usual, as soon as I post a problem report, I somehow manage to fix it
What I just did now was log into iCloud.com and I made a tiny edit to one of my notes (in my case, I deleted one line on a to-do list). Then I waited a few seconds for the data to refresh, and then I tried opening Notes locally again.
Let us know if this works.