From webmd.com:
Stevia and chemicals contained in stevia, including stevioside and rebaudioside A, are LIKELY SAFE when taken by mouth as a sweetener in foods. Rebaudioside A has generally recognized as safe (GRAS) status in the U.S. for use as a sweetener for foods. Stevioside has been safely used in research in doses of up to 1500 mg daily for 2 years.
Some people who take stevia or stevioside can experience bloating or nausea. Other people have reported feelings of dizziness, muscle pain, and numbness
Special Precautions & Warnings:
Pregnancy and breast-feeding: There is not enough reliable information about the safety of taking stevia if you are pregnant or breast feeding. Stay on the safe side and avoid use.
Allergy to ragweed and related plants: Stevia is in the Asteraceae/Compositae plant family. This family includes ragweed, chrysanthemums, marigolds, daisies, and many other plants. In theory, people who are sensitive to ragweed and related plants may also be sensitive to stevia.
Diabetes: Some developing research suggests that some of the chemicals contained in stevia might lower blood sugar levels and could interfere with blood sugar control. However, other research disagrees. If you have diabetes and take stevia or any of the sweeteners it contains, monitor your blood sugar closely and report your findings to your healthcare provider.
Low blood pressure: There is some evidence, though not conclusive, that some of the chemicals in stevia can lower blood pressure. There is a concern that these chemicals might cause blood pressure to drop too low in people who have low blood pressure. Get your healthcare provider's advice before taking stevia or the sweeteners it contains, if you have low blood pressure.