As one character puts it, power in Brave New World "is a matter of sitting, not hitting." Rather than use violence to enforce the law, those in power in this futuristic society have simply programmed the citizens to be happy with the laws. This power is bolstered by a free-flowing supply of drugs, the insistence on promiscuity, the denial of history or future as any alternative to the present, and the use of sleep-teaching at a young age to instill the irrationality of its choosing. This same power is limited only by those individuals who desire, for one reason or another, to be unhappy.
Helmholtz Watson is the most powerful character in Brave New World because he is the only one with control over his own mind.
The World State's power over its citizens is threatened most by man's instinctive desire for free will.