A number of insects attack rose buds, causing them to become deformed or fail to open. Among these are chafer, curculio, midge, aphid, budworm, and thrip. The symptoms you describe may also be caused by botrytis (mold), but the affected buds or portions of them usually turn brown or black.
Purple coneflower blossoms damaged by a disease called aster yellows often fail to develop properly and may have missing or dwarfed petals. Frequently, one side of the blossom is affected more than the other.
Here are links to more information about this subject:
http://www.extension.umn.edu/distribution/horticulture/components/6953_03.html
http://fairfield.osu.edu/hort/landlingjun19.html
Aster Yellows
