Why is the 32 cubes door broken in FEZ?
Solution 1:
The door you went through is not the real 32-cube door. The map location that contains the real 32-cube door is this:
As you can see, the pattern of room connections in this image is different from what you see in the question.
One relatively obscure thing about the Fez story, such as it is, is that some areas actually represent the same locations as other areas, but at different times. In a sense, the door you went through is the 32-cube door, but in the future, after it has become a ruin.