I can almost guarantee that this contains some duplicates, however, I would rather post all instances I found in one place than try and weed out the specific instances that have been reported already.

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Blocks affected: Glass, Redstone Block, Glowstone, Slab, Stair

Blocks used for testing: Repeater, Door, Pressure Plate, Button, Lever (top, bottom, side), Rail, Ladder, Trapdoor, Torch (top, side), Flowerpot, Redstone Dust, Fire (top, bottom, side)

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First image: Control. How we would expect blocks that must be attatched to other blocks to behave.

Glass: Non-solid block. Would expect it to support nothing, yet supports torches, just on top.

Redstone Block: Does not support Buttons or Ladders.

Glowstone: Supports only Redstone Dust and Trapdoor

Slab and Stair: Special case. Only thing I expected to work that did not is a lever on the bottom of a bottom slab/stair.