Use an internal redirect / don't show the user the /mobile part of the URL. This way, people who copy the link they have in their phone and send it to desktop users, they are greeted with the correct desktop link (otherwise, redirect them back?)
Show the room name etc etc by following the way the matrix.to code does it
I've implemented better mobile permalinks (i.e. the links that you share on the desktop web app should also work on mobile)
https://github.com/sipb/uplink/blob/master/server/var/www/matrix.mit.edu/mobile/index.html
There are two missing things:
/mobilepart of the URL. This way, people who copy the link they have in their phone and send it to desktop users, they are greeted with the correct desktop link (otherwise, redirect them back?)