What could bluish discoloration of the skin be?

Blue nevus. Another possibility is something called a blue nevus. This is a mole deep under the skin and because of the depth of the pigment it appears blue in nature.
Underlying veins. Blue discoloration can be caused by underlying blood vessels especially veins which contain deoxygenated blood. Underlying veins can make the skin look blue. Lack of oxygen in blood can cause blue discoloration. Raynaud's can cause fingers and toes to turn red, white, and blue.