Hi lulu!
Actually, radish is a hardy plant, it's even used as a companion crop with other vegetables because of its pungent odor in the storage roots that repels some common insects and even diseases.
However, there are some common pests and diseases that has the courage to attack by only mild.
Here they are:
Problem: Root Maggots
Affected Area: Root
Description: Leaves wilt and growth is stunted. Insect is common, white, root feeding maggot. 1/4" long adult flies emerge from the soil about the time cherries bloom and lay eggs at base of plants in surrounding soil. Legless larvae feeds on host plant for three weeks, riddling the roots with brown tunnels before they pupate Two or three generations can occur each growing season.
Control: Use Diazinon before planting as a soil treatment. Rotate from year to year.
Problem: Flea Beetle
Affected Area: Leaf
Description: Tiny holes ?pinholes? chewed in leaves by adult insect. Adult insects are 1/16" long, hard-shelled, shiny, dark-colored beetles that jump when disturbed. Slender, whitish, cylindrical larvae feed in or on roots but root damage is generally minimal.
Control: Dust with Rotenone. Keep debris removed. Rotate location of planting from year to year.
Some other suggestions please read talico33's post.
Happy gardening!
cris
www.crisramasasa.com