Point of View
Layers, like an Ogre
Have you ever stopped for a minute and asked yourself how sleep can be "deep"? It may just be an analogous way of thinking about sleep, but Nolan seems to take it pretty literally.
When talking about the different levels of dreams in Inception Cobb and the gang use depth as a way to distinguish levels. Reality is the surface level and our dreams are one level below. If we have a dream within that dream, it is even deeper, and so on and so forth until Limbo, which is about as deep as we can go.
To even further solidify the analogy, Cobb tells projection Mal that he will see his real kids "up above" as if the real world is very literally above him, even though he is at that moment located in the real world and only his mind has traveled.
It's important to have a sort of visual analogy to use with these dreams because Nolan has no qualms about cutting back and forth between them. That's not to say that Inception isn't chronological—in fact, the only flashbacks we get are Cobb's memories of Mal when he's telling Ariadne about what happened—but it's just that all of these different levels are happening simultaneously.
Hard Cuts
Transitions are a big part of the narrative process that filmmakers use to help tell a story. The transitions Nolan uses are cuts, meaning that we go right from one scene to another with no fancy fading or wiping in between. It's a very unobtrusive approach to splicing up a movie.
Think about the beginning of the French market scene. Suddenly we're sitting with Ariadne and Cobb in the market and we think nothing of it. They're talking and he's explaining dream things to her (and consequently to us). Then suddenly, he draws her—and our—attention to the fact that we don't know how we got to the market in the first place.
Movies, like dreams, can jump all over the place without us giving a second thought. Remember when Cobb travels to Mombasa? Of course not. One minute we're in Paris and then the next scene we get a shot of Cobb approaching a gambling Eames.
It seems totally natural (no one wants to watch Cobb go through security and board the plane and eat gross airplane food) but Inception makes us question how Cobb got to Mombasa and, of course, if the hard cut means he's actually dreaming.
However, there are many, many hard cuts… so perhaps the point is that we can't know and that, if we start thinking about it too much we become like Mal and like Cobb, obsessed with the idea that our world (or their world) isn't real.