Every conversation you have with the outgoing admin, record (with permission, of course). When they're showing you something a workstation, screen capture it. Write notes up for all of this the first while its still fresh. Have them walk you through each server, each device, and all the issue with it. You won't remember everything they've said, and they aren't going to do as great a job documenting things as you'd like during their last week, as they're head's already out the door.