I'm so super surprised no one has mentioned Super Mario Sunshine yet. That game was awesome, but it was rushed and had so many glitches in it.
For instance:
In pretty much every level, some way or another, you could end up falling beneath the entire level, and you would die if you didn't keep jumping.
In Gelato Beach, during the watermelon festival, when you're rolling the mega-watermelon past the giant mirrors, if you kill a Cataquack, the coins would go inside the trees and buildings and stuff.
Any time the Shine Sprite flies up and slowly comes down for you to grab, stand right underneath it and go into first-person. When it hits you, Mario will do his little dance, but the camera angle is all messed up, depending on which way you were facing.