Certainly, your characters - whether they are superheroes are not - should have foibles. They should have problems; they should have things that their powers can't solve. That's what makes them nuanced, interesting characters. They can have intense motivations. They should have intense motivations to do what they do.
My motivations are thinking I can write better songs, that the concerts can be better.
A good lie detector doesn't jump to conclusions but tries to understand the person across the table, her personality, and her motivations. Your goal as a lie spotter isn't to point the finger and say, 'You're lying' - your goal is to get to the truth.
