Remove all unpopped kernels from popped popcorn. Put popcorn in a greased 17x12x2-inch baking or roasting pan. Keep popcorn warm in a 300 degree F oven while making syrup.
For syrup mixture, butter the sides of a heavy 2-quart saucepan. In saucepan combine sugar, water, corn syrup, vinegar, and salt. Cook and stir over medium-high heat until mixture boils, stirring to dissolve sugar (about 6 minutes). Clip a candy thermometer to side of pan. Reduce heat to medium; continue boiling at a moderate, steady rate, stirring occasionally, until thermometer registers 250 degrees F, hard-ball stage (about 20 minutes).
Remove saucepan from heat; remove thermometer. Stir in vanilla. Pour syrup mixture over the hot popcorn and stir gently to coat, adding candies. Cool until the popcorn mixture can be handled easily. With buttered hands, quickly shape the mixture into 2-1/2-inch diameter balls. Wrap each popcorn ball in plastic wrap. Store at room temperature up to 3 days. Makes about 20 popcorn balls.