Snowball aphids, Neoceruraphis viburnicola, are notorious consumers of snowball viburnums and other types of viburnum. They cause leaf curl, feeding in clusters at leaf tips. Spray the shrub with insecticidal soap or horticultural oil to control these grayish-dark green insects.
The Clemson University Cooperative Extension service indicates that flower thrips, Frankliniella tritici and other thrips regularly invade viburnum. Avoiding insecticide is recommended because that also kills several natural enemies of thrips. Removal of or regular mowing of grass and weeds will help diminish the thrip population.
Regular, strong sprays of water, insecticidal soap and horticultural oil will help control spider mites on viburnum. Scales cause branch dieback and may eventually kill a viburnum. It is possible to manually scrape off scales, and it is important to prune heavily-infested branches.