Restone torches on piston power piston
Torches placed on the side of a piston will activate the piston, but according to the wiki, torches should not power the blocks they are on.
Linked Issues
The torch powering the piston is actually a bug. See MCPE-15195. Would be helpful to have a world download or more screenshots to understand more of what is going on.
Duplicate of MCPE-15195. (That bug report should be updated with the new burnout behavior that was introduced in either 0.15.3 or 0.15.4.)
This is definitely a bug. The block to which a torch is attached to should not be powered, and the block directly above the torch should receive strong power, but all other adjacent blocks should recieve weak power.
As demonstrated in Screenshot_2016-07-19-21-49-08.png, the block adjacent to the torch is only weakly powered, and so the piston should not be powered. If the block was strongly powered, the redstoen dust on top of the block would also be powered like the piston.
Perhaps this is related to MCPE-15195 & MCPE-16283 - they all involve redstone torches and pistons.

Still affects build 3
Confirmed for 0.15.0 official release. (Tested on Windows 10 Edition.)
EDIT: Also confirmed for 0.15.0 on Android.
Please respond and add the current version if you can reproduce this issue.
Confirmed for 0.15.4. (Tested on Windows 10.)
The behavior is different now, however. Previously the torches would simply power the piston. Now they blink rapidly, powering the piston, and then burn out, unpowering the piston. (As if they were in a torch-burnout-clock-circuit.)
Confirmed for 0.15.6 (Tested on Windows 10.) See above comment. The bug report's description should be updated to reflect the change in behavior since either 0.15.3 or 0.15.4.
Shouldn't this bug be closed since the new behavior is in
MCPE-16283? Or should that bug be closed and this one be updated with the new behavior?Yes. This one has been fixed in a sense. Closing as Fixed.