Quite a lot actually
Well lets see, HTML V5 is pretty much useless for web animation and web games, so all those are out, its an insane resource hog on anything without H.264 acceleration, so all your older PCs and phones and tablets? yeah those are out too. What else, oh yeah HTML V5 has baked in DRM thanks to Apple and MSFT, and only supports a codec that is one of the biggest patents landmines in history so Linux users? Yeah you can give up now, You have to be one of the big three (Apple, Google or MSFT) or you'll be committing patent infringment and with HTML V5 DRM so easy to use most videos? Yeah you aren't gonna be able to watch 'em.
Does Flash need a better alternative? Sure it does, its creaky and old and buggy as hell. But sadly instead of demanding something actually BETTER than what we have what is happening is corporate interests are ramming through a "standard" that is about as user friendly as the first XB-One press conference. There is a whole lot for big corps and big media to like about HTML V5, requires new hardware, has DRM, lots of lock in, for the end user? Yeah not so much, pretty much worse than Flash in every way, worse CPU and memory usage, worse codec support, worse game and animation support, nothing but worse all the way round.