This topic has been discussed here several times before. However as it's a topic I'm much interested in some thoughts:
Population: fairly obvious and already discussed above. But I'd add that we're unlikely to be able to change the fact that women are born with their full complement of ova; after around 50 years there are none left. So technology (eg freezing of ova - but how long can they be frozen for? Decades, centuries?) would have to be used to allow pregnancy after that. And that would allow direct control of those births. Ultimately you would have to have a system of one death one birth. I challenge anyone to do the figures on interplanetary or interstellar colonisation; whilst they may be good at removing all humanity's eggs from one basket they will never be able to cope with even today's rate of population growth. Just how long do you thing it would take to shift a billion people off planet?
Bodies worn out: Depending on how immortality is achieved there are many components of the body that could be a problem. For example teeth and bone joints worn out. So either we have to figure out how to get them to self repair or the immortal person might eventually end up more cyborg than human.
Memory: We really do not understand how memory works and we may never do so. The popular SF trope of editing your memory to 'make space' will probably never happen as the one thing we are pretty certain of is that memory is not managed as some simple linear sequential thing like computer memory. So do we reach a point where we simply can't learn anything new or do we constantly forget stuff to make room for new?
Work: as someone commented above, most of us won't want to spend a lifetime cleaning sewers. So we'll need the ability to completely change jobs. And, even after retraining into a completely different role, will we, after say 200 years, really want to go back to 9 to 5? Maybe not an issue if the much fabled post scarcity society is finally achieved (see also below).
Ennui: how many different jobs can you do, how many different adventures can you have, how many times can you fall in love before boredom sets in?
Hierarchy: whether it's family, military or business immortality makes progress almost impossible. Nobody dies or retires so no new opportunities open up for rising stars to fill. The prince/princess will never become the king/queen.
Risk: do we become risk averse because death means the loss of not decades but centuries? Or maybe ennui results in the opposite happening.
Religion: A few have mentioned religion above however one topic not mentioned (I think) is that most religions, to a greater or lesser extent, see death as being the time of final judgement. It is very possible that religious fundamentalists (and I believe there will always be a significant number of these) will see immortality as 'dodging' that final judgement and they are likely to take matters into their own hands...
Just a few thoughts to be going on with