To our knowledge, there are no "easter eggs" on any of the MST3K DVD's released by Rhino Home Video. However, there are some which feature former MST3K cast members hidden on discs released by other companies. These are the ones we know of so far.
This disc from Legend Films contains introductions from The Film Crew, aka Mike Nelson, Kevin Murphy and Bill Corbett. But there's a hidden "intermission" video not listed on the DVD's menu. Here's how to access it:
In the short "Malice in the Palace," the Stooges acquire a map.
While they're looking at the map for the first time, hit the Enter button. The video will play.
Joel Hodgson appeared in the episode "$20.01" which is included on this Warner Home Video DVD collection, so he was asked to provide commentary for it. Regular readers of this site know that Joel and his brother Jim also filmed new opening credits for the series that were never used. Now is your chance to see them! Here's how:
You will be given commentary options at this point to watch the credits with or without commentary from Joel.
(We will be providing screenshots for this easter egg at a later date.)