Coat two rimmed baking sheets with cooking spray then add an equal amount of popcorn to each one. Spread in an even layer then distribute peanuts and pretzel pieces equally over the popcorn. Set aside while you prepare the caramel.
Add butter, brown sugar, corn syrup and 1 tsp salt to a very large saucepan—the mixture will foam up and triple in volume. Bring to a boil over medium heat.
Once mixture has reached a full rolling boil, reduce heat to medium-low then simmer exactly 5 minutes, stirring occasionally.
Remove from heat then stir constantly while carefully adding baking soda, vanilla, and rum—the mixture will bubble vigorously and foam up, so be prepared! Drizzle caramel evenly over popcorn mixture then use two wooden spoons (like you are tossing a salad) to coat popcorn mixture in the hot caramel.
Once caramel has cooled enough to handle, coat hands with a little butter then form balls any size you would like. While they’re still sticky, sprinkle with a bit more salt if desired. Place popcorn balls on parchment paper to cool completely.
Once the caramel is cool enough to touch, work quickly—it sets up fast!