In 1984, why is the state of paranoia so important to the Party's system of control?
In 1984, paranoia is fundamental to the Party's system of control because it acts as a deterrent against breaking rules. When Winston first encounters the "dark-haired girl" (Julia), for instance, his paranoia is immediately apparent: he thinks she is a spy and he fantasizes about hurting her. In reality, Julia likes him and wants to have a relationship, even though this is against Party rules. Winston's paranoia, therefore, stops him from realizing her true feelings and, by default, from breaking this rule about forming relationships (until Part Two of the book, anyway).
Similarly, the Party uses children to maintain control through paranoia. This is shown in Part One, Chapter Two, when Winston visits his neighbors, the Parsons. The Parsons children are zealous supporters of the Party and, like other children in Oceania, are keen to report anyone who commits thoughtcrime. As Winston comments, there are countless stories in the press of children who have reported their own parents, which has created a climate of domestic paranoia and fear which keeps such parents in check:
It was almost normal for people over thirty to be frightened of their own children.