There ARE certain cases when particular people should not consume large amounts of fish or shellfish, mostly due to pregnancy or protein allergies. Your mother's concern, however, is probably unfounded.
Most fish, especially fish you would be purchasing, is farm raised in a monitored environment, so environmental toxins and pollutants, such as mercury and human wastes are not factors. If mercury and the like are a concern for your family, just be wary of wild fish. Some high end grocers do cary wild salmon and other fish because some people with discriminating tastes seem to prefer them. Fish and shellfish are a healthy way to get a low fat, high vitamin source of protein in your diet. The truth of the matter is that if Americans on average at 2 more meals of fish/shellfish a week, they'd consume far less fat and calories than otherwise.
Cooking fish and shellfish can be very easy, or more complicated, depending on your own abilities. To keep the health benefits of the food, I would recommend NOT deep frying/breading the fish; start with some simple recipes for baked cod, or maybe even baked farm-raised salmon cooked with grapes, apples, and garlic... DELICIOUS! Fish and shellfish are also an easy addition to soups, stews, and gumbos.
The great thing about fish and shellfish is that they cook up super fast, so the cooking is convenient, and they are SO healthy!
Bottom line: unless there are particular reasons for your mother's concern, fish are probably a safe, and healthy addition to your diet. The reason most common reason for people not including these foods in their diet is usually that they are just unaware of how easy it is... Its nothing to be afraid of! Put away the meatloaf, and try some fish tonight... you may be suprised!
ps- try a few kinds of fish before you decide you dont like it; different types carry different flavors, some have a more mild "fishy" flavor than others. i'd recomment trying tilapia, cod, whitefish, and then salmon, which is my favorite. also, i'd check out www.foodnetwork.com for some great recipes that are sorted out by level of difficulty. one more thing- i still get tripped up on the cook time of fish. dont overcook it, but do make sure its done by seeing that the fish has a nice, flaky consistency. also, it will lose the "shiny" look and have a nice, usually white opaque finish. good luck!
im just a foodie!