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.
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Most of this works as intended.

So you aren't going to note the ones that don't work as intended?

What's not intended has already been submitted.

Glass and torches: intended
Redstone Block: see MC-5850
Glowstone: intended
Slab/Stair: intended

You aren't supposed to be able to put levers on the bottoms of slabs when you can put them on the top? What's the reasoning behind that?

I suppose you can create a separate ticket for that case.

You should be able to put levers on the bottom of lower slabs and the top of upper slabs, but the other way around would result in the lever being half in one block and half in another, and that's something the game can't handle by its design.

Not quite. There was a mod a while back that allowed you too place torches on bottom slabs, by just lowering the mesh and bounding box by half a block. The torch itself was still technically in the block above the slab.