Constant exposure to a toxin (e.g. BT) or a herbicide creates evolutionary pressure for pests resistant to that toxin. This can reduce the intended effectiveness of the GMO in achieving higher crop yields in the long run and may lead to the evolution of “super pests” that are harder to get rid of.
There are concerns that one of the potential negative effects of consuming GMOs may be a spike in allergic reactions in humans. Since GMOs are a relatively new type of food, its effects may not be apparent yet.