I teach at BYU--in my interview with the GA, he had reviewed my vita and knew about my background and experience. He mentioned it briefly and then mostly we chatted about where I've been and he asked me to share my thoughts on the Savior and on my relationship with my wife.
The sense I get is that they are mostly just looking for the confirmation of the Spirit. They aren't looking for anything specifically, but just whether the Spirit indicates something is wrong with hiring a particular person.
Now before you even get to the point of having a GA interview, you are "vetted" to be approved for your interview with the department. I don't know what they do there either, but I'm sure they are looking for any flags on your LDS account and whether you currently hold a temple recommend and have for a while.