I just updated to 3.6 and I am having the very same problem with the menu.
Can’t drag and drop and a load of blank boxes the very same as colmstar’s youtube clip.
Every time I update wordpress there is a problem somewhere, the one before the widgets would not drag, big pain again.
I’m running wordpress with the smallbiz theme. A lot of work gone into the website so not really able to change themes.
Any tips to get around this menu problem will be a great help
Thanks