Steps taken to replicate the issue:
1. Open chest
2. Close chest
3. Perform various actions.
As of right now, I have no idea what caused the texture bug. The Z-fighting (there may be a more accurate name for this) of held items I can verify is caused by opening and closing a chest.

Going Home and using the Recent Apps Button to reopen MCPE stops all bugginess temporarily.

ROM: PAC-man for GT-P3110, built on 7/30/2013, Milestone.1.RC1