Proper Reflections -I'd call this a subtle improvement and a medium sized headache: It has to be a subtle improvement because we can't have any scenes where improper reflections look terrible, and it's a headache because we currently have a pretty optimised system for both culling and lighting objects that 100% relies on anything that needs to be seen, being visible in the viewport. So right now, objects behind you aren't lit, there aren't any shadows for them even if they were, and if you had one of those mirrors like they have in train stations, to see round a corner, you'd probably be seeing empty space. Anything that's calculated ahead of time would need to be much more conservative just in case a ray wanted to hit it later.
Proper Shadows - Better sharp shadows is actually something I think would be really easy for us to use this for, a ray per pixel per light in areas that were likely to have shadow aliasing would clean things up really well, without just cranking the shadow map resolution ever-higher. Soft shadows need quite a few rays per pixel per light, so we'd probably have to do something to restrict them only to the areas where there might be penumbra, and there would still probably be areas where a lot of the screen was covered by penumbrae.
Global Illumination - The very grandest of headaches! Diffuse GI needs a ton of rays to work well, I assume we'd have to cast them at a reduced resolution (either screen resolution or a sparse set of points in the world) and map that back to the full-res scene/geometry somehow (bear in mind that such things never work, they can just be massaged to fail to work subtly enough that things look ok), but even with that work done, we'd need a completely separate solution for non-raytracing users not to be left high and dry. Unfortunately, like with the fog I mentioned somewhere in this thread, a specific GI solution is exactly the kind of thing that influences what the lighting team can/can't do, so having two different systems with different strengths and limitations means compromising between the two, or having some extra features that let them change the lighting to fit the GI tech (possibly doubling their workload). I'm a big flag-waver for GI on our team, but I really think we'd be better doing something that's available to all users first, maybe with one eye open for how it could be accelerated or enhanced using ray-tracing later on.