The major implication of this idea is that there is nothing that is truly deviant, nothing that is truly wrong.
If we accept the idea that deviance is socially constructed, then we are saying that we believe that another society that differed from us only in its social values could believe that what we call deviant is really perfectly acceptable. This brings us into the realm of ethical relativism in which nothing is truly good or bad and such things are merely contingent upon what a given society believes.
However, this should not be seen as a major problem because the idea of deviance itself does not necessarily imply that actions are moral or immoral. It simply says that certain behaviors go against the norms of society. So, perhaps another important implication of this idea is that it should make us aware that various of our social norms are simply norms rather than objectively correct beliefs about what is right and what is wrong. This could encourage us to be less judgemental about some forms of deviance.