I took a video of a glitch i discovered last night. There is a golden cube that can be acquired in the beginning section of Fez. This chest normally contains a key once you've broken the hypercube and can shift dimensions in this section. But by performing a well-timed long jump, you can open this chest early in the game, and for some reason, it contains a golden cube instead of a key.
You can then open the door at the bottom of the level, but the fall damage has made it impossible to attempt to go through the door before acquiring the fez.
This seems like an unintentional golden cube, as Dot will glitch out during it's first appearance by shouting "You did it!" (the statement made when you successfully open the door) while it descends from the sky. Pressing B during this glitch will cause the game to become trapped between dimensions, and you will be unable to move until you restart the game. Waiting for Dot's monologue to continue properly allows you to continue the game normally.
I have not yet gathered all the cubes to see if this has any sort of impact on the ending.
If anyone discovers a way to get down to that door without dying, or if anything cool happens when you get 33 golden cubes, please let us know =]