Desaturation of academic (TT) job market in Mathematics and the Sciences
There are no "easy solutions" to this problem, but here are a couple things I have 


Increasing the funding in STEM fields. Essentially, with more money, you can hire more people, and keep the "game" going a little longer. This is what created the Clinton-era boom in STEM jobs in academia - a surplus of money allowed the creation of low commitment soft money positions in Universities. The drawback to this is, of course, that it doesn't actually solve the problem as much as delay it.
Decrease the number of STEM graduates. The replacement of a single tenure-track professor in a field at steady-state size is 1. Even for a field that's doubling in size, it's 2. That's a very small number of graduate students who can actually be expected to find tenure-track positions coming out of a lab. Reducing the number of graduate students being produced stops this overpopulation problem. The problem with this solution is that you have a little bit of a Tragedy of the Commons problem - its really best if everyone else do this, and you don't, resulting in you having a massively productive lab. Right now, much of academia is built on large amounts of graduate student labor, and reducing the number of graduate students would mean figuring out a "new normal" for lab productivity.
Non-academic jobs. This is, essentially, where those students above replacement rate end up - but right now, many people in STEM view this as a lesser position, or a failure. That's not particularly realistic, and the fields would probably be well served by making sure that their grad students were aware of those options, and well-prepared for them. Some fields do better with equipping their students with transferable skills than others (biomed is particularly bad). The problem with this of course is that it's relying on tenure-track faculty to view the path they didn't take as one worth pursuing, and educate themselves on those options.