Bonus Feature:
The first disc, for example, contains an unannounced, isolated music and sound effects track of the film. Simply select 'About the Music' in the disc's "Main Menu" and then select 'Musical Themes'. A list of music titles appears with Chinese numerical indices. Select the indices and you will have the chance to see the corresponding scenes with the music only.
Reported by: JonRobertson,IanPang, EdwardDittman

Music Video:
Another hidden feature is located on the second disc of the set. From that disc's "Main Menu" select the 'About The Cast' menu entry, and from there go to Tony Leung Chiu-Wai's entry. On the first page of his biography press your Up button to highlight a music note. Now press your Enter button and you will see a music video for Tony Leung's song 'Hua Yang Nian Hua' that was directed by Wong Kar-Wai.
Reported by: JonRobertson,IanPang, EdwardDittman

Trailers:
Also on the second disc you should go to the 'Wong Kar-Wai: The Searcher' section. Here you will find detailed notes about the director's career, complete with hidden trailers for Ashes Of Time, Fallen Angels, Happy Together and In The Mood For Love. All you need to do to access them is to go through the various pages of information and at the end of each section the according trailer will play.
Reported by: JonRobertson,IanPang, EdwardDittman