Place the peppercorns, coriander, clove, and allspice into a spice grinder and grind for 10 to 15 seconds.
Fill a 40-quart pot with 5 gallons of water and add the freshly ground spices, salt, cayenne pepper, garlic powder, paprika, onion powder, thyme, oregano, dry mustard, dill weed, and bay leaves. Cover and bring to a boil over high heat, approximately 40 minutes.
Rinse the crawfish thoroughly in the bag in which they arrived to remove excess dirt and mud. Put the crawfish in a large container and fill with cool water. Stir to remove dirt from the crawfish. Transfer small batches of crawfish to a colander and rinse under cool running water. Pick out any debris or dead crawfish. Once all crawfish have been rinsed, discard dirty water, and return the crawfish to the container. Repeat this process 6 to 8 times, or until the water is clear.
Once the seasoned water comes to a boil, add the potatoes, corn, garlic, and sausage. Cover and cook for 10 minutes.
Add the crawfish, cover, and cook for 3 minutes. Turn off the heat and allow the pot to sit, covered, for 10 minutes. Drain well and serve immediately.