If countries set limits on the amounts and types of pesticides used in growing food, why do they need to test for residue? Wouldn't any residue be within limits if the companies were following the law? Those are common and understandable questions, but that's not quite how pesticide use or non-use works. Crops grown without pesticides can have residue on them, parts of a plant that were never exposed to pesticides can still end up with residue inside them, and manufactured products can be subject to cross-contamination. This is why pesticide residue testing is so important to know when something's gone wrong.
Contamination Through Wind
Pesticides that are sprayed on crops can be carried on the wind to nearby fields. This can result in both excessive exposure and exposure to a pesticide that the nearby fields shouldn't be exposed to. For example, unexpectedly strong winds could kick up, and before the person spraying the pesticide has a chance to stop, some spray may get blown into the next field. If the crops there have already been treated, then they could end up with excessive exposure and more residue than is allowed.
Cross-Contamination With Treated Food Products
During processing, transportation, or storage, one food can become contaminated with residue from another food, and that other food could have pesticide residues on it. This can happen in a factory or processing facility where machinery processed different foods. This is also an issue with organic fruits and vegetables, too, as non-organic items that have residue on them can accidentally mix with the organic ones that are not supposed to have exposure to pesticides. Random testing can check if this cross-contamination has happened.
Translocation Within a Plant
Sometimes pesticides are sprayed on part of a plant and get into that plant's tissue. The process of translocation, which is exactly what it sounds like, ferries the residue to other parts of the plant. For example, a carrot grown underground might not have direct exposure to a pesticide sprayed above ground, but if that pesticide gets absorbed into the leaves, translocation can ferry residue to the root portion.
Finding pesticide residue does not always mean the crop is ruined. There are tolerance limits that allow some exposure in many cases, and some pesticides are legally allowed on a number of crops. But testing should reveal those cases where the residue is excessive or not allowed, and your customers will appreciate that you're trying to prevent unallowable residues from reaching them.