The first thing to get, is that for most people, most of the time, not dying is a really good thing – worth all manner of “problems”. I am certainly in that class of people.
It became clear to me in 1974, as I completed undergrad biochem, that indefinite life extension was possible; and it certainly comes with many problems given all the many levels of biological and social systems we have evolved for living relatively short lives (70 years or less).
Extending life spans will, in the not too distant future, mean being healthy and with fully functioning bodies – so all the losses of function we currently associate with old age will disappear.
That does require some changes.
If we are to keep the population of people on earth to levels that allow everyone a reasonable standard of living, then we will need to reduce the average family size to one child per couple. At that the population would eventually double from the size it is when that policy is instituted. If we get really efficient about our use of energy, and do most of the heavy engineering in space using remotely controlled automated systems, then we could comfortably house about 20 billion people in what most today would consider a high standard of living (good food, safe warm housing, great healthcare, reasonable travel (a world trip every year), reasonable freedom etc. The technical issues to delivering such an outcome are trivially simple compared to the social issues of changing the way people behave towards each other and their environment.
To live in such a world, to have such security and choice and freedom, demands of every one of us responsible behaviour in both social and ecological contexts – and that becomes a very complex set of issues as we are dealing with many levels of awareness.
So in this sense, of increasing life expectancy to the extent that most people would have a reasonable expectation of living for thousands of years, then the major problem will be creating awareness that everyone must accept and protect diversity (far more diversity than currently exists, and exponentially increasing), and everyone must act responsibly in both social and ecological contexts – and neither of those things can be easily quantified – both will be eternal explorations of novel territory, and such exploration can never be free of risk.
So for many people, particularly those on the extreme end of the conservative spectrum in any dimension, it is likely to be a little (or a lot) uncomfortable.
Some people may retreat to conservative havens where the more novel entities are barred from entry unless they disguise themselves as conservative entities and behave as such while there. So the nature of the boundaries that are likely to evolve will probably be very complex, even by the standards of the most complex social structures present today.
And it does seem to be achievable, but not in a world where markets have any significant role in the measurement of value. The scarcity based nature of market values is not compatible with the abundance based systems that are both possible and necessary with fully automated systems, and that transition is likely to be very difficult for many.