It could be small. But it would be the sort of thing that the dreamer could not ignore, once he'd observed it. It could be something as simple as...hmm. As simple as, "these walls are blue, but I know they're supposed to be red"! Even something like that, so long as it's wrong, could be enough. What makes the difference is what happens after you notice it.

[She shrugs a little, finally relenting enough to reach for her own breakfast.]

If the wrongness fades away, or you start to ignore it, then it isn't a real dream. If it wakes you up, it isn't a real dream. But if the dream persists despite the wrongness, then it's much more likely to be true.