I've been wondering what makes an item have an inscription slot. Is it random or is it the place where the item dropped that makes it have an inscription slot or not, or maybe something else?
It's the place where it drops. Items dropped in Tyria (Prophecies) don't have an Inscription slot. I don't recall at the moment whether Factions items have inscription slots. Nightfall and EotN items do.
Almost any "skin" can pop out of Dungeon chests (and the Zaishen chest) with an inscription slot.