I'm integrating Jstree with QMT and it's working perfectly with the addition of nesting the $before_title and $after_title within a list item within an unordered list. I may also need to insert an ID into what become the root "folder" links per se, and I'm using the default theme, with no dots and no icons, so that there aren't weird ins elements between the term-title and the add/remove anchor.
However, I'm attempting to use the cookie feature in order to keep the "folders" open that have already been open when the page is refreshed, but, when I implement it ( which I could be doing totally incorrectly because I'm not a cookie master ), the Jstree functions disappear completely from the page. All it takes is including the ui and cookie plugin in order to make jstree not work, so, should probably tackle that before tackling the fact that I am probably not implementing the cookies correctly.
I think I may also run into an issue with the fact that on initial selection, the template changes to multi-tax. I'm not sure if that would affect the cookie or not. Still to be determined once I can get rid of the fact that just calling the cookie plugin breaks jstree.
Beyond that I have also tried using the core: initially_open options ( after inserting an id of jstreeterm before class="term-item" ) and that hasn't worked either.
So, the base use of Jstree is awesome, and I highly recommend using it with QMT, but, it would be great to get the cookies and initially open options working.
More than happy to give a login Scribu, if you're interested in taking a look ;-)