Firstly: As you stated in your response, well designed organic and agroecological systems negate the need for synthetic toxic pesticides and fertilizers by designing a combination of cultural methods and functional biodiversity into the systems to provide the ecosystem services that control pests, diseases and weeds.These are the tools of first resort.
Secondly: In some cases, as natural systems can fluctuate, it many be necessary to use natural products of plant, mineral and biological origins to control pests and diseases. Mäder et al. showed that the use of these products are 90% less in organic systems than pesticides in conventional systems. These are the tools of last resort.
All of these products rapidly breakdown, leaving no toxic residues. They do not have be toxic. Examples of very effective treatments are emulsified vegetable oils, mild soap and flour and water. These work by smothering the breathing pores on insects and are not poisons. There is no evidence that small residues of natural vegetable oils or flour and water are toxic to people, otherwise we will have to ban salad dressings and bread etc. Similarly all the evidence suggests that regular exposure to mild soap and water is good for people. I always advise farmers to start with these three first, as properly used they can control all pests.
Toxic sprays such as natural pyrethrums should be used with caution, as they can effect the producer when they are being used, however they degrade in 24 hours leaving no residues for the consumer.
Most diseases can be prevented by correcting the soil structure with good levels of organic matter and correcting mineral deficiencies. Simple spays such as compost teas, milk by products, natural sulfur, lime etc along with appropriate cultural controls such as correct pruning etc are generally sufficient to control all diseases.
In my 40 years in organic farming in more that 100 countries on every arable continent, I have not come across one pest, disease or weed problem that we cannot manage effectively with the appropriate organic systems. It is only ignorance of good organic systems that makes people reach for the poison bottle.
Andre Leu, president, International Federation of Organic Movements, September 2014. email to F.M. Lappe