What do you mean by "What does she rule?" Are you asking what she presided over/ what her office was as a deity? If so, she was the personification of retribution or righteous indignation. According to the Dictionary of Greek and Roman Biography and Mythology, "Nemesis is a personification of the moral reverence for law, of the natural fear of committing a culpable action, and hence of conscience... In later writers, as Herodotus and Pindar, Nemesis is a kind of fatal divinity, for she directs human affairs in such a manner as to restore the right proportions or equilibrium wherever it has been disturbed; she measures out happiness and unhappiness, and he who is blessed with too many or too frequent gifts of fortune, is visited by her with losses and sufferings, in order that he may become humble, and feel that there are bounds beyond which human happiness cannot proceed with safety. This notion arose from a belief that the gods were envious of excessive human happiness". I don't know that she helps the modern world in any particular way.
She is among the many fatherless children borne by Nyx, the personification and goddess of Night, although she is sometimes said to have been sired upon Nyx by Erebos, or she was a daughter of Okeanos or Zeus.
Sometimes depicted as a winged goddess, her attributes were an apple tree branch, a [horse's] rein, a lash (or whip), or the balance (scales).
Like just about all the other Olympian deities, she could disguise herself in the form of various objects. Zeus is said to have lusted after Nemesis but she avoided his advances upon her because he was her father. She tried to escape him, changing herself into various animals as she fled, but he imitated her transformations and gave chase, until she finally became a swan, and he, taking the same animal form, caught up with her and raped her. Some time later she laid an egg which she gave to Queen Leda of Lakedaimon. Helen later hatched from the egg and was raised by Leda and her husband King Tyndareos as their daughter. Leda was also said to have been an incarnation of Nemesis, or she became Nemesis after she died. Helen was apparently born so that the conflict she would bring into the world would thin out its population, which was getting out of hand in Zeus' opinion. And hence the balance represented by Nemesis would be restored.
Beyond that story she's too much of an abstraction to be defined as possessing any weaknesses.
Aaron Atsma, The Theoi Project, on theoi.com