On Disc 2, on the main menu, press your Up button on the remote to highlight the musical note, press your Enter button. You will now get to see a karaoke video featuring various characters singing bits from various songs such as "YMCA", "Who Let The Dogs Out?" and so on. This is the same karaoke video that is on Disc 1, but its not mentioned on the Disc 2 special features.
Go to "Special Features", on the bottom of the screen highlight "Main Menu" and press your Up button on the remote to highlight the Gingerbread Man's buttons, and press your Enter button You will be taken to the "Fun Facts" screens. This is mentioned on the package, but does not tell you how to access it. This works on the "Special Features" menu on both discs.
On the main menu press your Up button on your remote. This will reveal a new icon at the top of the screen. On disk one, it's the Dreamworks Kids logo that leads you to another menu with favorite scenes, "Shrek's Music Room", and "The Game Swamp" with a few more games than the regular one. On disk two, it's a musical note that leads you to "Shrek's Karaoke Jam", something already disk one.
All easter eggs were generously submitted by SirDonk