Place shrimp in a saucepan. Add water, Old Bay, and vinegar.
Place over medium-high heat. Stir frequently. When shrimp have turned completely white, they are done. You may see 1 or 2 start to float. This is a sign that they are done. The water may not come to a boil. Do not worry about this. You do not want the shrimp to overcook. If you are unsure, pick one up and gently squeeze it. It should feel firm.
Run cold water over shrimp to stop cooking. Let cool and then peel shrimp.
If shrimp are on the larger side, cut them in half or thirds.
In a medium bowl, stir together mayonnaise, lemon juice, onion, celery, and Old Bay.
Add shrimp and mix them in. Sprinkle dill on top.
If desired, Sprinkle a little more Old Bay on top. Serve immediately or refrigerate.