What would count as interesting times in the fictional world you've created? What is a normal state of affairs (politically or otherwise)? What would be seen to rock the boat? How would the "establishment" handle a major upset? How would they treat the one(s) creating that upset? The way someone is treated says a great deal about the person/system behind the treatment after all.
I could see there being many a fine story in characters causing upset accidentally. An action of theirs sets in train reactions and consequences so how would they feel about this? Would they try to limit/undo the damage, get the hell out of there fast before the authorities come after them, or be unrepentant about the whole thing?