Is an impurity found in an aspirin tablet likely to be a problem?
Absolutely, but how significant is the impurity?
How concentrated is the impurity? At some point, the analyst is going to declare that the aspirin is analytically pure, and at this point the impurities are simply along for the ride. Quality control is (clearly) taken very seriously in pharmaceuticals; they don't want to sell a contaminated product, if only because they wish to prevent law suits, but of course they don't want to harm anyone - life is easier that way.