Minecraft – rule that means mobs spawn on slabs

You don't have to obstruct every area in your enclosed redstone circuits. You can easily place normal torches and/or Glowstone blocks throughout the enclosure. This will also aid in visibility within your ICs. Redstone can be placed on glowstone blocks, but they exhibit interesting properties, so be careful

Redstone can be put on glowstone, but being a transparent block signals can pass from one block to diagonally another with glowstone "blocking but not blocking" it, making possible nearly instant vertical redstone and new vertical logic gate designs.

Well, indeed mobs don't spawn on glass or slabs (half-blocks). The way you describe it, that spider couldn't have spawned on the roof. There is not much more to say without actually seeing the house and its surroundings. Is it possible that the spider tracked you from outside and climbed on the roof (unlike other mobs, spiders can track you through walls)? Is it possible that the spider spawned on a nearby cliff or tree and fell on the roof?