When standing on a bottom slab (i.e. not a full block) the light level on the F3 screen will be 0 (0 sky, 0 block) even when standing next to a block. This also applies to the bottom step of the stairs.
As far as I know only slabs and stairs have this problem. Daylight sensors, chests, repeaters don't seem to be affected, but I haven't tested this extensively.
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Confirmed.

14w11b still has this issue, if I can, I'll attach my screenshot. I'm even standing next to a glowstone block!
Edit: Screenshot added.

Still an issue in 14w28b

Still an issue 14w30b

still in 14w30c

Also in 1.8-pre1

Confirmed for 1.8,
Attatched screenshot.

And 1.8.1

Also in 1.8.3

This bug appears to apply to the lower step of stair blocks as well.

Can anyone confirm whether this affects mob spawns?

Mobs do not spawn on half slabs or stairs.

Bottom stair/bottom slab light of 0 confirmed for 1.8.7.

Can also confirm for 1.8.7....

Affects 15w31a

Confirmed in Minecraft 1.8.8

Also affects path blocks

I'm closing this as working as intended: When you are standing on stairs/slabs like this, you are inside the 1x1x1 block boundary. Light level inside blocks is 0, so it should display 0.

What about the aforementioned path blocks though? Also, the light level on carpet, snow or a bed is just fine. Beds, slabs and carpets all behave the same when you place another block on top of them. Is there a significant difference other than the (visual) height?

The blocks you listed do not block light. Path blocks are solid, but not full height.

This also happens on farmland, which is actually a problem, because light level affects how crops grow.

There is no problem for farmland. This ticket is about the displayed light level on the debug screen (which is in fact zero when the player is inside blocks) but the actual light level internally used by the game for crops, spawning mobs etc. is correct.

Yes, I understand the mechanics of what's going on. The farmland is slightly shorter than a full block, putting the bottom of the player's feet in the farmland block, so the debug screen is showing the light level of the farmland block (an opaque block at light level zero), and not the light level of the crop block.
While this effect is rather benign for grass paths, light levels when walking on farmland is not. Light level affects crop growth, and not being able to read that from the debug screen poses a game play problem.

The debug screen is not meant to be used for gameplay.

This bug has been fixed in 18w46a.

Fixed for everything other than soulsand; I've created MC-139631 for that since soulsand is a bit of a weird case.