What are the advantages of blood's redness?
The reason why blood is red is rather simple: It is the iron atom in the middle of the heme, which plays the central part in binding oxygen. Depending on the oxidation state the blood looks either dark or light red. The structure is the following (taken from here):



That the color only depends on the coordinated metal atom is shown by another related molecule, the hemocyanin, which is the oxygen carrying molecule in the hemolymph of insects. It contains copper which is colorless in one oxidation state and blue-green in the other. The function is the same, the color is different.