The sociological problems of immortality are more difficult than the technical problems. The entire sweep of human history has rested upon the same solid foundation: death takes everyone eventually. Kings fall down as dead as peasants, and the dirt nap of a saint lasts as long as a sinner.

Imagine what would happen if the people who held certain beliefs never died off. Imagine the result if large estates never passed to any heirs, or debts never cancelled. Imagine copyrights that never expire, since the authors never die. The young, vital, and innovative do not prosper, since they are forever dominated by their elders who become increasingly conservative and risk-averse. Money and power do not pass from one generation to the next.

The problem is only made worse if biological immortality is itself an expensive product that is only accessible to the wealthy. Down that path I can imagine dozens of dystopias.