Well, it's a very very rare complication, and one that dentists know how to and should avoid, but if the anesthetic substance reach a blood vessel it may cause problems with the functions of the heart (mainly the heart rhythm, less commonly the normal heart attack).
However, if you have heart problem, especially problems with the valves of the heart you should inform your doctor and your dentist - you may need to receive antibiotics prior to the dental procedure in order to prevent infective endocarditis (infection of the heart valves).
You may read more here:
http://www.nlm.nih.gov/MEDLINEPLUS/ency/article/0010... http://www.nlm.nih.gov/medlineplus/dentalhealth.html 