In a 2-cup glass measuring cup stir together tomato juice, pickle juice, horseradish, Worcestershire, hot sauce, lime juice, vodka, ½ teaspoon of the celery salt, and ¼ teaspoon of the ground pepper until well combined; set aside.
In a small bowl mix together remaining ½ teaspoon of celery salt, remaining ¼ teaspoon of pepper, and the dill; transfer to a small plate and gently shake to distribute.
Rub lime wedge around the rim of 10 oz glass. Turn glass upside down, place rim on plated salt mixture so that it sticks to the rim.
Turn glass upright, pour tomato mixture into glass. Serve chilled.