A specific concern I've always had about this idea of indefinite lifespan is that of monoculture. How often have you heard a phrase along the lines of "this is a temporary problem; once the 'old guard' is no longer in charge, society can move forward on issue XYZ"? Make "XYZ" any major social issue we've had in the past thousand years; from fiefdoms to gay rights to democracy.

It's effectively the end of generational cultural change, which might be a good or bad thing, depending on which generation you most identify with.