Big Brother takes control of his people via extreme brainwashing of his populace. Everyone is taught that the government's priorities come before the people, and that the government decides the truth.
He destroys all evidence contradicting what he wants his population to believe, and if anyone attempts to upsurp his government, they are killed, and all evidence of them ever existing destroyed.
Despite the fact he is not really omnipotent, his population believes that the truth is whatever he says, and therefore he could say he was flying and everyone would believe it.
Another issue is the fact that BB can die. However, if he was to die, he would be replaced with a new one.