Most any organic matter can be composted, but there are some materials that should be avoided. Meats, bones, fats and oils are very slow to decompose and will draw unwanted pest. Sawdust is best left out of the pile if there is any chance it is from treated (CCA) lumber. The arsenic, copper and chromium used to treat the lumber will become a part of the finished compost and eventually, whatever is planted in it.
Pet wastes can contain pathogens, and although the high temperatures of a well-managed compost pile will kill most diseases, they should never be included in the pile. Pet wastes can be buried at a depth of at least 8 inches, but only in areas where food will not be grown. The consistent heat of the compost kills many plant diseases, but it is hard to tell if it has been completely eradicated.
If you suspect a plant is diseased it should not be included in the pile. Pernicious weeds, such as morning glory, ivy and some other plants and grasses can resprout from their roots and/or stems in the compost pile. It is usually best to leave them in a sunny, dry place for a few days to make sure they are completely dead before adding them to the pile.