Explosions, hazmat spills, beer replication without a license. ..
...are the things Doc and company have interacted with the local police, fire departments, Alaska National Guard, State Troopers and numerous federal regulatory and enforcement agencies over the fifteen years. Sometime during all their misadventures they had to acquire at least misdemeanor arrests. In fact, didn't Roger say at one time he had to bail Doc out and vice versa?
Heck, I had a couple of minor misdemeanor arrests on my record and still received a Top Secret security clearance when I was in Army Military Intelligence. Yes, the FBI and Defense Intelligence Agency knew about them (I had to list all schools attended-fun when you move every three years or so; Dad was Air Force-ALL jobs from age fifteen to twenty-six, all arrests excluding traffic, marriages and family members) before they started their background investigation. I can imagine Doc and Roger have the same clearances and Sandy, Pirta and Swampy have been investigated due to their employment there. Jinx is too young, but his family might have been checked. My family was checked even though Dad had a Secret and my brother (Captain, USAF) had a Top Secret clearance. They used to check EVERYTHING back then!