I believe children should be given fish to eat despite warning about mercury levels. Fish is perfectly safe in small quantities and all fish is not contaminated by mercury. I think it is better to allow children to eat fish rather than risk the chance of them being allergic to it later on down the road from lack of exposure.
For adults, I would say let them make their own choices. But children, who are still developing and need balanced nutrition more then adults because of that, I say no. Unless there is a study done that can show that mercury at certain levels doesn't harm a child's development then I say it should be taken out of their diets completely.
Fish does have mercury in it, and mercury isn't the kind of thing you want to consume. It needs to be mentioned that some fish has way more mercury than others. The fish at the top of the marine food chain typically is where the mercury tends to be concentrated. Fish like tuna contains loads of mercury. I think that generally speaking the health benefits of diet that includes fish as opposed to red meat outweigh the dangers of mercury.
Yes, children should be given fish to eat despite warnings about mercury levels, because mercury levels are not so bad that it would cause any real damage for children. Fish is generally healthy. It has a large amount of B vitamins, and other vitamins and minerals that help children grow.