Could jumpiness be a major mental health problem?

Perhaps. Some people are just a little anxious, but it doesn't impair their ability to function. However, "jumpiness" or increased startle response could be a sign of posttraumatic stress disorder. It could also indicate that a person is very tense as a result of anxiety. I'd say if it a person finds the jumpiness is causing problems functioning then it would be worth consulting with a psychologist.