The Flynn effect, as I understand it, is the finding that IQ scores have been consistently raising over time, and around the world, indicating each successive generation is more intelligent than the one which came before it. Flynn himself believes this is probably not quite as simplistic as it seems; for, if that were precisely true, we would be experiencing a worldwide renaissance in all areas in all places. Instead, he believes we have increased in such areas as problem-solving and abstract thinking, making each generation more adept at thinking, though perhaps not actually more intelligent.
Your question is what disadvantages and advantages accrue to society because of this increase. Of course, the increase itself is neither positive nor negative--it simply is. There are, however, some positive and negative ramifications from this increase.
On the negative side, older people are often seen as being less intelligent than younger people because they have lower IQs. Traditional thinking has been that we lose intelligence as we age; instead, when IQ scores for the elderly are aligned with scores during their own growing-up time, they are just as smart when they're old as when they were young. The perception, though, is that our older population is just not as bright. Unfortunately, that is true to this extent--the world is more and more complex, and those problem-solving and abstract thinking skills which everyone else has improved are still more of a struggle as we age. (Think about older people having trouble programming their TVs or phones or VCR/DVD players, or whatever.) As the younger generations gain in those areas, the older generations will struggle to keep up with their innovations.
On the positive side, improvements in abstract thinking and problem-solving are the root of all innovation. Society can only benefit, it seems to me, from a population which can think and reason. Children and young people are exposed to and experience so much more opportunity for intellectual stimulation today than ever before, and that will certainly pay off in better thinkers for the future. Some of that stimulation (such as video games) has other negatives (such as childhood obesity and inactivity), of course; however, in terms of increased IQs, society wins.