"Does either a tatare sauce or deep frying get the mercury and DDT out of the fish?"
Nah, it just masks the sickly sweet flavor of the DDT and the bitterness of the mercury. ;-]
In the real world, I don't eat anything deep fried, and there are lots better options than tartar sauce for accompanying baked potatoes, braised Black Cod, Sockeye Salmon, etc. To be honest, though, it is hard to avoid picking up at least traces of mercury, DDT, PCB's, etc. The pernicious stuff is endemic just about everywhere. I was surprised back in the late 70's to read a report that wildlife biologists in California had detected DDT in the fat of trout from high altitude lakes in the Sierra interior. Apparently it was carried up there attached to soil particles by prevailing winds off the San Joaquin Valley just to the west. The stuff had long been banned, but it persisted in the soil long after. All one can do is try to minimize their exposure by careful dietary choices, but even then there are no guarantees.