Go to Special Features, from the main menu, and select The Dream World. Highlight and select the red pill at the bottom of the screen to see a feature on how they did the 360 degree camera rotation.
Also from Special Features, select Cast & Crew and highlight and select Written and Directed by the Warchowsky Brothers. This will bring up another red pill that when selected will show the process of concept to final filming.
There are also clips of behind the scenes footage that you can access by selecting white rabbits that appear throughout the movie. After you select the rabbit, and the footage is shown, the movie will return to where it left off. To activate the rabbits, go to Special Features, select Making the Matrix, then select The Dreamworld, select Continue, then select Follow The White Rabbit and the rabbits will appear when you play the film. There are nine white rabbits.
Different versions of movies are routinely released on DVD, for different regions, special editions, and so forth. Eggs listed for a specific movie may or may not work on other releases, so feel free to give them a go.