Pistons are incorrectly activated when adjacent to a block that is adjacent to a power source that emits activation power (except for redstone blocks, which seem to be a special case), but the block is not powered by the power source.

Confirmed to affect pistons that are adjacent to blocks that are adjacent to redstone torches, observers, buttons, levers, pressure plates, and detector rails.

Ironically, this bug causes pistons to be powered by observers as if observers output strong power instead of activation power. So this bug actually makes observers more consistent with the Java edition when it comes to pistons. (They still only technically output activation power, though, so this is a piston bug.)

To Reproduce:
Place any block that strongly powers at least one other block and pay attention to the blocks that it also activates.
Place pistons adjacent to the activated blocks taking care to ensure they are not adjacent to any strongly powered blocks.
Observe that the pistons (regular or sticky) activate when they should not.

We dug a bit deeper and have determined this bug affects both regular pistons and sticky pistons.

This bug affects any power source (redstone torch, lever, trapped chest). Basically any block that powers at least one other block. This bug does not affect blocks that merely activate other blocks (i.e. redstone block, buttons).

Original Report: A torch can power a piston sideways through a block. The torch can power the piston sideways no matter how it placed. The torch sends power through the block but the block is not powered.