In a small bowl, combine the butter, dill, and garlic; season with salt and pepper and set aside.
Fold four 14-inch squares of heavy-duty aluminum foil in half, forming 4 rectangles. On one half of each of the four rectangles, arrange potatoes in a single layer, then top with cod, then shrimp. Place 2 pieces of the corn on the side. Season with salt and pepper. Add a dollop of the butter mixture and two lemon slices. Fold foil over ingredients, and crimp the edges tightly to seal.
Place the packets on the grill, with the potato layer on the bottom. Cook, rotating (but not flipping) packets occasionally, until the fish is just cooked through and the potatoes are tender, 12 to 14 minutes.
Carefully remove the packets from the grill. Slit the packets open and transfer the contents of each packet to a plate. Garnish with dill sprigs.
Serve with some good bread to soak up all of the juices.