Well usually when this happens there is also a ventricular septal defect and a patent ductus arteriosus. These secondary defects make life possible as they provide a way for oxygenated blood to reach the entire body.
with the vessels backwards and those secondary defects not present, blood would never get re-oxygenated. the lungs would also be a closed loop with the left side of the heart. The reason there is cyanosis is that the blood is coming from the body (vena cava) and then pumped out to the body again (right ventricle pumped to aorta in trasposition). The septal defect and patet ductus make it possible to mix in some oxygenated blood (but still no where near normal)
total guess, but it could be due to a PDA distal to the left-subclavian.
A baby with great vessel transposition can survive for a short time only if there is an ASD, VSD, or PDA. If there is no way for the blood to mix, the baby will probably be blue all over. Since the high-pressure is in the pulmonary circulation (coming out of the left-ventricle) blood flow across the PDA would be reversed from normal. So if the PDA were distal to the left-subclavian, oxygenated blood would flow from the left-ventricle -> pulmonary trunk -> PDA -> descending aorta, bypassing the upper-limbs and causing the infants fingers to be bluer than the toes.
like I said, just a guess! A PDA usually causes differential cyanosis with the toes turning blue and the fingers remaining normal. With great vessel transposition it could be reversed though because the blood would flow from pulmonary to systemic circulation.