Place scallops and shrimp in simmering salted water; cook 1 minute or until just opaque. Drain completely.
Arrange scallops and shrimp in a single layer in a large shallow glass or ceramic dish.
In a medium bowl combine lime juice, oil, onion, tomato, radishes, and salt and pepper to taste. Mix well. Spoon lime juice mixture over scallops and shrimp. Cover and refrigerate 30 minutes to 1 hour.
Spoon scallops and shrimp into individual glass dishes. Serve with avocado slices and cilantro sprigs.