The world may be becoming overpopulated. But I don't think anything major needs to be done about it (such as controlling birth rates). Things will sort itself out eventually.
I figure a few things will happen which will make the point moot.
1: The population will even out naturally to where its a 1:1 birth/death rate...or less of a birth rate but which will pick up again eventually as the need warrants it.
2: World War which will make the last two pale in comparrison thereby reducing the world population drastically. (hopefully in such a way as to not destroy humanity all together)
3: We will expand into space in which case overpopulation just will not be able to happen as people will go to other places which has more room. Perhaps even make generational ships to travel to other star systems. (assuming that we haven't cracked some way around FTL travel)
I consider #2 to be the most likely to happen with #3 running a close second depending entirely upon situation. #1 being possible but not likely.