다치다 is being injured, and -면 states the risky condition: overdoing your workout, one careless move, messing about. 까불면 다쳐 is a half-joking threat — muck around and you'll get hurt. 잘못하면 and 자칫하면 are the standard 'if you slip up'. One line uses it figuratively, about a topic that hurts you if you dig into it too deeply.