Fill a large pot with water and bring it to a boil.
Add the baby potatoes to the pot and cook for 10 minutes.
Stir in the Old Bay seasoning, garlic, and salt.
Add the corn pieces and cook for an additional 5 minutes.
Add the mussels and clams, cooking until they begin to open (about 5 minutes).
Finally, add the shrimp and cook for another 3-5 minutes until they turn pink.
Once all ingredients are cooked, drain the pot and return the seafood and vegetables to the pot.
Gently toss everything together with lemon wedges.
Transfer to a large serving platter or newspaper-covered table.
Serve hot with melted butter on the side for dipping.