Arterial blood isn't "pure". It is simply in one part of a complex circuit which carries varying degrees of oxygen, nutrients, and waste products, etc., to varyious parts of the circuit.
...how are these waste materials getting into the arterial blood?
The most simple and direct (but teleological) answer to this is that toxins need to get into arterial blood to ever get to the kidneys to be filtered. The arteries carry blood to every part of the body, detoxifying organs included. Veins carry blood away. If there were no waste products in arterial blood, the kidney would be superfluous.
Waste is produced in all tissue. Blood carries oxygen and nutrients to the tissue (where some of it is used), and via the venous side (all over the body) blood carries the waste products (as well as unused oxygen and nutrients) away toward the heart. The blood carrying waste products collects in increasingly larger veins until it is dumped into the right side of the heart and pumped into the lungs, where a major waste product (CO2) is partially removed. Things that need to be removed by the kidney are all still there. Blood carrying these toxic products is dumped into the left side of the heart, and thus enter the arterial blood supply. The kidney then can remove waste products partially or completely when it reaches them.