Could genes escape and cause problem?  Gene transfer from crops to other plants is now called “gene flow.”  What you need to know is that plants have to belong to the same species in order to trade genes.  Plant genes travel either in seeds or in pollen. Some crop plant seeds can be readily dispersed by birds or by trucks carrying grain, but this rarely results in the establishment of crop plants in the wild, simply because the traits that allow plants to survive in the wild have been bred out of them by people over thousands of years.  But pollen is carried by the wind and by insects and could, in principle, pollinate wild relatives.  Cross-pollination is a familiar problem for farmers and particularly for seed producers.  For example, a little patch of sweet corn is grown in the middle of a field of fodder corn, the farmer won’t get much sweet corn, because the surrounding starchy fodder corn plants will pollinate them and produce starchy kernels. Canola, which is a rapeseed mutant that produces a healthful oil for humans, can cross-pollinate with closely related strains that produce an oil that isn’t good for human concumption.  Farmers must be careful not to plants these too close to each other. So cross-pollination is not a new problem for farmers. 

Whether genes from crop plants can be carried to wild plants by pollen depends on the plant.  Corn, for example, has wild relatives in Central and South America, but not in North America or most other places it is grown.  So the first requirement is that there be a local weed species that can cross hybridize with the plant in question. But canola does have wild relatives where it is grown in Canada and England.   The other question that needs to be asked is whether the transferred gene could cause a problem in the wild plant population.  Herbicide resistance, for example, is a potential management problem for farmers, but probably of little concern in the wild where herbicides are not used.  These are the kinds of issues that the U. S. Environmental Protection Agency (EPA) and the U. S. Department of Agriculture (USDA) consider when they approve new crops.  To date, this has not surfaced as a major management issue for farmers. So far, transfer of GM traits to wild relatives has not been observed to be a significant problem.