Before leaving my previous institution, I participated in a project (http://indicatorsproject.wordpress.com) that was starting to look at using LMS data.
Initally, we we're looking at Blackboard v6.3 and a local system. Then the institution adopted Moodle and that's where focus went.
Getting access to the data from the LMS was very simple technically, but very difficult politically. The technical task was made simpler because the project included a couple of folk from a technical background.
Most of the initial work was simply looking at the data and figuring out what useful patterns could be identified.
I've moved on from the institution, however, the other participants are continuing and that includes a "student success intervention" based on an application that attempts early identification of student failure.
Colin Beer (http://beerc.wordpress.com/publications-and-writings/) is the driving force behind the project.