There are some well-known counterstrategies, but experience indicates they eventually will fail. So we need to carefully monitor insect pests for resistance and continuously develop alternative control strategies. A third hazard is that crops such as Bt corn will harm beneficial insects. Recently pollen from Bt corn was shown to kill caterpillars of the Monarch butterfly. Nevertheless, this case demonstrates the need for more detailed monitoring of the effects of Bt crops.
Allergies are the most significant one.
Transferring genes from one plant to another may introduce new allergens in foodstuffs. Known allergens can be tested for, but there may be surprises. Other fears have less scientific basis. There's no a priori reason to suppose that ingesting pieces of DNA transferred from one plant to another is any more hazardous than ingesting the large amounts of DNA we get every day from numerous sources in normal diets. European consumers, especially in Britain, have eagerly jumped on the anti-GM bandwagon, while so far those in America haven't.