Remove all unpopped kernels from popped corn. Place popcorn in a greased 17x12x2-inch baking pan. Keep popcorn warm in a 300 degree F oven while making cinnamon mixture.
Butter the sides of a heavy 1-1/2-quart saucepan. In the saucepan combine sugar, water, red cinnamon candies, vinegar, and salt. Cook over medium-high heat to boiling, stirring constantly with a wooden spoon to dissolve sugar and cinnamon candies. This should take about 6 minutes. Avoid splashing mixture on sides of pan. Carefully clip candy thermometer to side of pan.
Cook over medium heat, stirring occasionally, until thermometer registers 270 degree F, hard-ball stage. Mixture should boil at a moderate, steady rate over the entire surface. Reaching hard-ball stage should take 20 to 25 minutes.
Remove saucepan from heat; remove candy thermometer from saucepan. Stir in oil of cinnamon, if desired. Pour the cinnamon mixture over the popcorn; stir gently to coat the popcorn. Cool until the popcorn mixture can be handled easily. Use buttered hands to shape the mixture into 3-inch-diameter balls. Wrap each popcorn ball in clear plastic wrap. Makes about 10 popcorn balls.