From what I've learned during past two years of running 64-bit Debian GNU/Linux, there is no difference in stability, and no significant difference in speed. Compatibility issues exist mainly with proprietary components such as Flash you already mentioned, but also with some open source applications -- few even come from official Debian repository. However due to number of problematic applications this is hardly a show-stopper for everybody.
Debian comes with several 32-bit compatibility libraries which allow running most pre-compiled 32-bit executables. When this isn't enough, 32-bit chroot can be set up. Setting up the chroot isn't a problem, but maintaining it is just another unnecessary annoyance. 32-bit applications can be run transparently from "pure 64-bit" environment, but it requires some manual work.
Speed difference? I have this feeling that some applications run slower and some run faster. Generally speaking there is no difference, but multimedia-related tasks seem to benefit from me. While I wrote this artice
about how optimisation with GCC switches won't do the trick, the figures also to tell about differences between 64-bit and 32-bit applications.
All in all I'd say ordinary user doesn't want to run pure 64-bit GNU/Linux just yet. Masochists like me can choose otherwise.