Be particularly careful about spraying for dandelions when trees and shrubs are in leaf. Do it in the spring when the dandelions are growing fast, just before trees leaf-out. Fertilizers most often represent an opposite situation to weed killers and other chemicals. Far more damage is done to trees by not using them than by overuse or misuse. In fact, I can't recall ever seeing many trees suffering from overfertilization.
Insecticides are dangerous.
They contain poisons. They are formulated to be as safe for humans as possible, but they still contain poisons and must be used according to label directions. Insecticide formulations can be dangerous to humans and pets an d can do both direct and indirect injury to landscape plants. Direct injury may be either physical or chemical. This potential problem was, of course, clearly stated on the label.