Relates to 1.5 "Redstone Update"
http://www.youtube.com/watch?v=nfBVAexor3s (From 0:40 onward. If the video does not work, an attachment has been added to counter such removal.)
The attachment's "Sandstone" slabs are powered from a redstone torch underneath the stone block. Redstone torches cannot power half slabs.
What I expected to happen was...:
Half-slabs not carring signals via upward staggered placement (Shown in picture.)
What actually happened was...:
Instead, the redstone current is sent up the staggered placement of half-slabs.
Steps to Reproduce:
1. Look at attached image or see linked video above starting from 0:40
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Added a few things to make it "Clearer" even though it's exactly the same as it was before.

This is not a bug, but a feature request, and should be posted on the MC forums here.
This is definitely a bug, when it breaks redstone logic.

This behaviour follows directly with redstone logic (see minecraft wiki here. Because the block is opaque, redstone current will travel up (but not down) half-slabs.
So it's not a suggestion either. How do you suppose I go about this then?
Made a modification request instead I guess:
http://www.minecraftforum.net/topic/1589558-request-redstone-realism/
Work As Intended.
Clarification on why this works as intended: Redstone current can pass through the block because it is transparent (this also works with glass). So each piece of redstone is actually connected to two different pieces on the same side. It doesn't work downwards because slabs do not conduct redstone.

@unknown That doesn't explain why it connects logically (not visually, at least not fully) at all. It should either not connect and not transmit power or connect and transmit power in both directions.
Hmm, yeah that doesn't make much sense. Now that you can place redstone on glass, the issue is even more apparent there. The wire shows as connected (even up the side of the glass) but redstone current can only be sent up. Feel free to review.

Review? What do you mean? You're the mod, only you can mark for review.
I'm not the one who resolved it and it was resolved many years ago, so I'm not going to reopen it. Mojang can certainly review this bug if they want.

I've heard a few times of a mod-only field that marks a report for review for Mojang. I have never seen how this worked, but probably another moderator knows that.
This issue ticket is not very clear. Please follow this as a guidline.