I'll try to polite. This is intended - the demo mode is designed as a way of new users being able to play a small part of the game, with the restrictions of a predetermined world, only 90 minutes and survival mode only.
You can, however, open your world to LAN with cheats and if you have another user with a premium account, they can change your gamemode to Creative (as far as I know).
I hope this helps.
I can confirm this happening on my game too.
I have iPod touch 4th generation, iOS 6.1.
I can confirm this bug.
Also, when I tried it with an in-game screen recorder mod, it crashed the game when recording.
Confirmed on SMP in 13w37b.