Eat young fish. Typically, in a given body of water, mercury level in a fish is directly proportional to its age. Avoid, if you like, large fish (e.g. tuna, marlin, swordfish, shark) and small fish which take a long time to mature (orange roughy, grouper, etc), but don't be afraid of all seafood.
Coincidentally, eating small fish is much better for the marine ecosystem as well. They are much more difficult to overfish (not that humans haven't figured out how).
Not that coal is the source of all of our ills, but I have read that to elevated levels of mercury pervading the environment are primarily from coal plant stack emissions. Given this, I wonder why it isn't a diplomatic issue between, say, Japan and the US or Japan and China?
It is. Reducing China's dependency on Coal is a huge priority for both China and the international community. It was a big point of discussion during last year's talks at Copenhagen.