When using the Filtered List search (http://jquerymobile.com/demos/1.0/docs/lists/lists-search.html) and the Bubble Count (http://jquerymobile.com/demos/1.0/docs/lists/lists-count.html) in the jQuery Mobile interface the bubble count number doesn't auto-populate/auto-update. This is something you need to add yourself. It would seem to me that this should be simple enough to do myself and with a little event binding this can all be fixed.
I ran across another issue when trying to filter a list using jQuery Mobile's Filtered List (http://jquerymobile.com/demos/1.0/docs/lists/lists-search.html) The functionality itself is really nice, jQuery framework does all the heavy lifting for you. All you need to do is create a <UL> or <OL> and add the attributes data-role="listview" data-filter="true" to the tag and your off. The problem I encountered, I wanted to programmatically execute the filter. On my page I had a number of re-populated search terms that I wanted to provide the users. Clicking on the button would pop the search string into the search input box. The problem was, adding the search string to the box wasn't enough. It required some event to trigger in order to filter the list down. After digging around and trial and error I found that a simple keyup event in the search box worked.
I am starting to get my feet wet with jQuery Mobile and find the lack of documentation frustrating. I will be patient as I know that this is a new framework. But to help anyone running up against my frustration I will start posting issues and solutions that I have come accross.