From my high school AP Art History class, I believe that door is where the priest would enter. I vaguely remember something about a controversy when it was revealed that Michelangelo put the depiction of hell in the lower right (directly above the door) with the tormented characters pointing at it.
For the life of me I can't find verification of this online, though, so hopefully Mr. J (my APAH teacher) wasn't just making it up.
Edit: Ahh wait, I think you were talking about a different door. Mine is a smaller black door in the lower right of The Last Judgement.
This was not the tourist exit, and inside there were huge beautiful golden hallways with exquisite paintings all around.
Does anyone know if this part of the chapel is visible or recorded anywhere?