Maybe you could try Online to find a member of the FBI you can ask questions of - like what you might have missed or what you can do to improve, i.e. what really shines on the application process and what doesn't.

You could put up a question on Yahoo! Answers and sites like that to maybe get some feedback from someone who is actually FBI and knows what to do.

Also, I wouldn't sweat it too much. From what I understand there is a backlog of applicants to federal jobs. hell, jobs everywhere. I just lost out on two job that I was definitely qualified for (interviews went great too!). Both companies told the contractors I would have hired through that they liked me very much but just had other available candidates with even more experience (one I used to work through and I admit he is even better qualified than me). So many people have lost jobs and are now willing to transfer around there is just a huge pool of highly qualified candidates. So, it might not have been anything you did just more so that there were people who scored higher.

But, definitely try again in six months!
Also, you know about usajobs.gov? It might be a step into government work.