It seems incredible that one could dream about a non-existent idea in such detail as I sometimes do. How could one dream about reflecting on it and discussing it with others, if there never was any real "it" being discussed? Did the dreamt discussion not involve any specific words combined meaningfully into sentences? Perhaps not. At least, the specific snippets I remember from such dreams seem far less coherent when exposed to the unforgiving light of wakeful reflection. (Perhaps there really is an idea, which simply lacks the brilliance ascribed to it in the dream, but it's not entirely clear where to draw the line between jumbled incoherence and no idea at all.) I've previously suggested that dreaming is like a form of anosognosia, in which we're unaware of our cognitive deficits. It could seem like a dreamt "idea" or "discussion" is brilliant, simply because the lack of content evades our diminished awareness.
Compare Brandon's account of William James' experiments with nitrous oxide:
While on it, he had the intense conviction of having discovered the secret of the universe, the ultimate discovery that would revolutionize the way we look at the world. So he wrote it down. When he came out of the state induced by the gas, he found that all he had written down were a few puns.
(My favourite: "That sounds like nonsense, but it's pure onsense!")
Our initial puzzle may in part be due to the misleading common-sense picture of conscious experience as providing a kind of direct and infallible grasp of the "sense data" found inside our minds, on display in the Cartesian Theatre. On this view, one's total conscious experience simply consists in the direct appreciation of all the specific contents that are presented on this metaphorical stage. Hence, to dream a conversation, that conversation must really be taking place on your mental stage, for your mind's eye to observe. I don't know if anyone would explicitly endorse this view, but there's something intuitive about it, and this explains some of the pull that we (at least, I) initially feel towards the idea that dreamt ideas are real in a way that dreamt actions are not.
This idea is strongly undermined once we re-model our understanding of consciousness in terms of representation (rather than presentation). Representations can mislead in a way that direct presentations cannot, for there's a sense in which only the former can hide its component parts. On the presentation model of experience, as described above, we are aware of everything that's on stage. Each specific element is transparent to us. But if dreamt experience is merely a representation, then things are rather different. Representations can be fuzzy or incomplete; you can represent that Sherlock Holmes has hair, without there being any particular number of hairs that you thereby represent him as having. Likewise, you might dream that you have a conversation or idea, without there being any particular conversation or idea that you dreamt about. Rather than being built up from specific component contents (e.g. real words combined into meaningful sentences), the impression that is one's "total experience" might be irreducibly superficial. The appearance of richness and depth in dreamt experiences may be entirely illusory. The stage might be empty after all.
On an extreme form of this view, we might even be lead to the conclusion that we don't truly experience (e.g. visual) sensations whilst dreaming -- we merely think we do. I wouldn't want to go that far, though. I do think that dreams involve genuine phenomenally-conscious representations, it's just that the contents may misrepresent other elements of our awareness. A dream may involve the conscious representation that I'm aware of a great idea, when in fact there is no such idea that I'm aware of at that time. It's all an illusion. But just because there's nothing really on stage, doesn't mean that I don't have subjective experiences to the contrary. Again, it's just that the experience misrepresents itself as being deeper than it truly is.
Let's consider two opposing examples to finish up. First: dreamt fluency in a foreign language you don't really speak. I've heard such dreams may occur (though I haven't had one myself), but they obviously misrepresent the dreamer's actual thoughts, which cannot truly involve fluent sentences of the alien language. So that supports the above suggestions.
Here's a harder one: music. I often dream that I can compose/improvise incredibly beautiful piano music on the spot. Alas, this is not a skill that I possess in my waking life. But don't the vivid auditory experiences in these dreams arise from my imagination? Isn't my subconscious the composer of these spontaneous beauties? Hence, don't the dreams entail that I do, in some sense, possess the dreamt skill after all?
To apply my earlier response, we would have to assert that there is not actually any real tune, or sequence of specific tones, that I auditorily experience in these dreams. The stage is empty. I have a dream experience which represents there as being a beautiful tune; but in fact the details are never filled in, and in my diminished state of awareness I never notice the lack. Is this plausible? I find it extremely difficult to swallow, since the dreamt experiences sure seemed to have more depth than that -- a depth that I thought I apprehended. The appearance of vividness was very compelling, at least in the sense that I am initially no less inclined to trust it than any other memory about an episode whose specifics elude my recollection. (And - I say, clutching at straws - the reality of it would not be so impossible as in the foreign language case.) But, I admit, it is probably wishful thinking to resist the application to this case...