Fish
You have probably already been cautioned against consuming certain types of fish, from Tilapia to genetically engineered salmon, for a number of reasons.
It is unfortunate, because fish have some of the healthiest forms of proteins and fats you can consume. But the caution is justified, so care must be taken.
I'm just highlighting two types here, but the principles mostly apply in general.
Organic Fish
There is no such thing as organic fish. The environment can't be controlled well enough to ensure that fish will only consume an organic diet or swim in fully sanitized waters; and even if you could raise them in a totally isolated tank, it is doubtful they could be provided with all the ingredients that makes them such a healthy food to begin with.