Good question, I'm curious about that too. But the only thing I can think of is DRM-protected QuickTime/iTunes files won't work in the 64-bit version of MC even if you have QuickTime installed, mainly because QuickTime on Windows is no longer developed (nor do I think Apple ever released a 64-bit version of QuickTime). I really don't think that's too much of a loss, since there's nothing JRiver can do about that one and if you're using MC to play DRM-protected files through QuickTime, I'd highly recommend obtaining DRM-free versions of said files if possible.
I'm sure there's nuances with 32-bit VST plugins not having a 64-bit counterpart, which isn't a MC issue. And possibly ASIO drivers from some manufacturers only coming in 32-bit and not 64-bit which, again, isn't a MC issue. Perhaps scanners too if you use MC to scan stuff, which *may* not work in the 64-bit version, probably depending on drivers so one would have to try it. I guess there's also the possibility some handhelds may not work with the 64-bit version of MC which do work with the 32-bit version but they should mostly work. Somethings to keep in mind, I guess.