Yes, some people do eat dolphin. According to the Sea Shepherd Conservation Society, dolphin meat is sold in Japan. However, it is often mislabeled as whale meat, and it is "almost always contaminated" with environmentally dangerous pollutants.
The Japanese government is not required to warn its citizens about the hazards of eating dolphin meat. In 1999, scientists conducted tests on dolphins and small whales to determine the toxicity contained in the meat. The samples revealed the presence of methylmercury, PCBs, DDT, a chemical used in insecticides, and cadmium, a carcinogenic metal. Of the samples tested in the study, 91exceeded accepted limits in one or more pollutants. One sample alone had 1,600 times the maximum amount of mercury permitted by law.