Production and Research overflow in Civilization 5

Solution 1:

As of the 12/15/10 patch, research should overflow as it did in previous civs. Any extra beakers that weren't needed to learn your tech will be applied towards your next one. Carry over on production still does not overflow. It can be abused to some extent, so they may have intentionally eliminated it.

Solution 2:

As of the 12/15 patch, research carries over between scientific advancements, identically to the past Civ games.