This demonstrates a problem with the serialization of nested lists in the jQuery UI Sortable tool. If you press the serialize button to see the current output and then move If you move "our" after "Ipsum" in the nested list and press the button again, you get the same output. These two different structures should serialize differently.
I've posted a solution of sorts for my particular problem. But it doesn't really fix the main issue.
(The serialize button logs to the Firefox console if it exists or just does an alert if the console doesn't exist.)