BBC have updated their iPlayer application to add compatability with Jelly Bean, as well as switching to the new 'BBC Media Player' utility rather than depending on Flash.
While this is good news, everything is not as great as it seems - the BBC Media Player appears to use Adobe Air internally which is rendering it incompatible with some devices (Medfield based devices for instance) and while the application does work, only low quality streams seem to be available at the moment (despite the changelog claiming 'improved video performance').
So... it's a start, but the BBC really do need to step up their game on Android. Still no high quality streams, still no option to download shows. :(
Head on over to the Play Store to download the update.