I found a description of the glitch in another forum. This is the copied text:
Glitch 1) Beat the game with 16 stars.
To perform this glitch start a new game and play through it until you have 15 stars (so that MIPS the Bunny appears in the basement), now head to Bowser in the Dark World and defeat him so you obtain the key to the basement of the castle. Now head down there and grab MIPS. Now take him to the door you came in through, that leads back to the room containing the 30 star door. Now you need to perform the 'take MIPS through doors glitch'. For those unfamiliar with this glitch here's a brief description;
Drop MIPS as close to the door as possible, then walk through the door. As soon as Mario has finished the door opening animation turn and jump back at the door. If you get the distance just right you should land merged with the door, if this happens don't move or you'll open the door, instead, press B to grab MIPS. Now turn and drop MIPS on the other side of the door.
Now grab MIPS again and take him to the 30 star door and drop him a short distance from the door. Now turn around and face away from the door and jump between MIPS and the door, if you get the distance right you should be bumped straight through the door and into the room behind.
Now you need to enter Dire, Dire Docks and complete the first star to uncover the entrance to the Bowser in the Lava Sea course. Beat this bowser to obtain the key to the first floor of the castle.
Now you'll notice that you're trapped in the the room with the entrance to Dire, Dire Docks, to get out simply enter DDD and pause the game and select Exit Course to appear back in the castle lobby. Now walk up the stairs and through the locked door to the first floor of the castle.
Now you need to use the backwards longjump glitch to get through the the 50 star door. To perform this glitch stand at the bottom of the stairs facing away from the door and longjump towards the camera, now hold down Z and tap A when you touch the ground to keep longjumping. While doing this push the analogue stick towards the door, you should start doing backwards longjumps on the stairs. When you land on the stairs, continue to hold Z and the analogue stick and begin rapidly pressing A. With luck you should start moving at a high speed and fly through the 50 star door.
Now make your way to the endless stairs and do the same thing. You should easily make it to the top where you can enter the Bowser in the Sky course. Now simply beat Bowser and you're done! You've completed the game with only 16 stars, less than one quarter of the original amount.
I am gonna try this now. Took me a while to find the stairs glitch thingy, the rabbit glitch was rather easy to find (not to perform though)
