Let me first say that I have had lucid dreams and I am aware of the unique dynamics they involve. The example that follows is nowhere near that level of awareness. However, I think it does involve some similar "self-split" mechanism (on a lower level?) that is intriguing to note.

Opinions welcome

I was dreaming a scene with some British police officers. At some point, they're after someone and they're pulling out their guns. I was "within" the scene in the dream, as an observing character, and I thought "Hey, hang on. That's wrong. British p.o. don't carry guns". The scene/dream went on as if nothing happened. I'm not 100% sure whether I thought "Hey, this must be a dream, this detail doesn't fit" or simply "hey, this is wrong, this detail doesn't fit". It was a bit like watching a movie and seeing the mic hanging for a second or two - it violates the "world creation" level.

In any case, I think it's interesting that we can spot inconsistencies like this. I can't call it "lucid" or even "pre-lucid" (especially since the dream went on as if nothing happened), but I think it does touch on the surface of "split consciousness" or "split world" if you'd like.