Until now, the assumption behind how Remembering the Kanji worked was in the order the kanji were presented. By systematically learning the very simple kanji that make up the complex kanji, one could make everything easier to remember.
"It will soon become apparent that the most critical factor is the order of learning the kanji. The actual method is simplicity itself. Once more basic characters have been learned, their use as primitive elements for other kanji can save a great deal of effort and enable one to review known characters at the same time as one is learning new ones." Introduction to James Heisig's Remembering the Kanji
I do not want to belittle the effectiveness of the order he presents, but the true brilliance of his book was the systematic deconstruction of the kanji. Being able to see any visual component of the character and immediately recognize it as something familiar. I myself can attest to this, having memorized kanji in an order that was of no benefit and sometimes even contrary to my efforts, since using this method requires learning kanji in groups of onyomi (learn all the kanji pronounced KAI as a group, for example).
The process to learning kanji out of order is a simple one, but requires preparation. The student must learn the visual components and assign them meanings before beginning any study of the kanji. The components to memorize are the basic and simple shapes that cannot be composed of other kanji, of which I have counted 209 so far. Memorizing these is an easy task, because the average Japanese student will be familiar with quite a few shapes already, and because the student can choose the meanings to suit their needs. I have a list of these components, and will gladly share it if I am able to find a place to host it.
Because the Movie Method places emphasis on locations to place images, instead of stories, it becomes a simple trick to learn kanji out of order. Combinations of kanji that appear together will earn an essential image that is reused in every kanji that it appears again. For example, in the kanji for 'morning' [朝] there are four components (vs. Heisig, which would only give two). When I first saw this kanji, I had never seen the specific combination of components on the left before. But by breaking it down and creating mnemonic images based on groups of primitives, I created an essential image (for me, it's a stereotyped sun as a pillow with two large syringes sticking out of it) that I can reuse in other kanji. By doing this I may have four components, but it becomes moot because I only need to work with two essential images. It becomes apparent that the reason this works is precisely the same as why Heisig's order works. We both recognize common combinations of components, but we recognize them at different times. Heisig acknowledges his primitives by assigning them concrete meanings beforehand, I acknowledge them by assigning them concrete images in an informal way as I go along.
Here is a more complete example using Heisig's assigned meanings for the basic primitives. In the movie Ocean's Thirteen (my location for KAN) there is a scene where a character is packing his things in his car to leave a hotel. When he opens the trunk [幹], he has to use one hand because is syringed sun pillow is under his arm (his luggage, I suppose). Inside the trunk of his car however, there is an opened umbrella with potatoes pouring out onto the street. [I have learned that 'potatoe' is actually 'dry' as one of Heisig's primitives and as the kanji meaning. Memorizing all the components before knowing the kanji can be a little weird when explaining things.]
This entire scene is played out in my mind in only a fraction of a second that I created in mere moments. I only present it here as a logical story for understanding, because when I create stories I only think of how I can incorporate the component images into the scene that's already set up to play out. When I use scenes in my head to remember kanji, I need only add my kanji components to the scene that's already playing out, even if it's totally illogical.
Need some concrete examples? Sample movie - Pulp Fiction.