Most of these chemicals break down after several weeks, and should not be used within a certain timespan before the crop is harvested, so that humans do not ingest the various chemicals.

from Microsoft Encarta 96 Encyclopedia, ref 3.
DDT, colorless chemical pesticide, dichlorodiphenyltrichloroethane, used to eradicate disease-carrying and crop-eating insects. It was first isolated in Germany in 1874, but not until 1939 did the Swiss Nobel Prize-winning chemist Paul Müller recognize it as a potent nerve poison on insects. First used heavily in World War II for preinvasion spraying, DDT was disseminated in great quantities thereafter throughout the world to combat yellow fever, typhus, elephantiasis, and other insect-vectored diseases. In India, DDT reduced malaria from 75 million cases to fewer than 5 million cases in a decade. Crops and livestock sprayed with DDT sometimes as much as doubled their yields.
With the publication of the American marine biologist Rachel Carson's Silent Spring in 1962, suspicion grew that DDT, by entering the food chain and eventually concentrating in higher animals, caused reproductive dysfunctions, such as thin eggshells in some birds. Some insect pests also gradually developed DDT-resistant strains whose populations grew unchecked while their natural predators, such as wasps, were being eradicated by spraying. In 1973 DDT was banned in the U.S. except for use in extreme health emergencies. Many other nations have also banned it or placed it under strict control.

Current Situation. Many environmentalists and ecologists are concerned that these chemicals interfere with the food chain, as in the above example of DDT. Current concerns in the UK are that frogs are dying, and that the population of sparrows is greatly reduced. Slug pellets have been suggested as a possible cause of both of these, though these are generally used by gardeners not farmers !
There are other ideas that modern monocultures are 'unnatural', and inevitably insects and weeds with fill 'ecological niches' which are vacant. Nature abhors a vacuum !

Future. Modern techniques of analysis are able to detect many type of contamination, and at very low levels. However, the costs of testing are high, and the systems are slow - products are often marketed and consumed before the results are ready. Food testing for chemicals and residues will certainly increase in future ! The use of plants with disease resistance my lead to future improvements, but there are concerns that if this result is achieved by genetic modification, then there may be other consequences on other species which are not predictable.