Insert DISC ONE and from the Main Menu go to the 'Language Selection' Submenu. Here, move to the entry for English Subtitles and then press [Right] to highlight the Image of Bruce Willis. Press [Enter] now and you will get to see a Credit Screen.
On DISC TWO go to the Main Menu and press [Up]. If you press [Enter] now, you will see an explosion of the Nakatomi Building from The Film, which in real life actually is the 20th Century Fox Office Building, followed by the line 'There Goes Fox Home Entertainment'.
From DISC TWO's Main Menu select 'From The Vault' and then 'Outtakes.' Then select 'The Vault' and on the next screen press [Right] twice. This will highlight a small gun on the screen, which will give you the chance to watch the Outtakes with Music Only.
All easter eggs were generously submitted by Bjorn_K