Common pests of broccoli include aphids, cabbage worm, and flea beetle. (See "Broccoli in the Garden" at http://extension.usu.edu/files/publications/factsheet/HG_Garden_2005-01.pdf

Cabbage worm is actually a caterpillar, so it can be controlled with the organic control Bacillus thurengiensis (B.t.). One trade name of this product is "Dipel", but it is also available from other companies under different brand names. You can read about B.t. and how it works at the Colorado State University Extension website, http://www.ext.colostate.edu/Pubs/insect/05556.html

Flea beetles are common in spring, but usually cause insignificant amounts of damage, so control is not needed. Read more about flea beetles at Colorado State University Extension's webpage: http://www.ext.colostate.edu/pubs/insect/05592.html

Good gardening!