First check you're running the last Telegram version, that's 2.3.36.2
Second, have you tried to delete the cache (.cache/com.ubuntu.telegram)? That will erase your secret chats too, so you can make a copy before deleting it.
Yup, latest version. I tried clearing the cache and no change. Since I was in console, I just checked syslog and I'm getting a dbus DENIED. I'll poke at it when I have more time, but I wonder if they need to fix up their apparmor perms.
Curious as to why your getting a different result though.
EDIT: I'd also be curious as to your opinion of Touch in general?
My opinion: I love it. I'm not a huge fan of Unity, or Ubuntu, and it's definitely in the beta stage. I like that most of the problems that I have were solvable on my own via shell-script or whatever hacks I come up with.
Once in a while I got a blank screen opening Telegram, but closing it and open it again solves the problem.
Are you running OTA-15?