Several species of fish, like pelagic sharks and swordfish, have unsafe levels of mercury and are no longer considered good choices by the FDA for human consumptions (Read FDA advisory). Man-made contaminants can work their way up through the marine food chain until they deposit themselves in animals of commercial value.
Many organizations, like Oceana.org, have lobbied grocers and major supermarket chains for years to post the FDA advisory for its customers. A recent participant has been the major food wholesaler, Costco. The advisory provides important information as to which fish are safe or unsafe - not just a blanket warning against all seafood, which would probably not gain much credibility with the general public.
Ironic that the potential for limiting the commercial demand for sharks and swordfish - which could help in their conservation - comes about due to our poisoning of these animals beyond safe limits. Maybe we should irradiate the Amazon rain forest so that the wood could no longer commercially be safely used for paper or building materials. Crazy logic . . .