Deleted Scene: An unfinished scene that was filmed shows that Destoroyah was to have the ability to fire an energy beam from his chest known as the "Wave-Motion Ray". He was to fire it 1-2 times on Godzilla with it. It was ultimately scrapped due to it's little usage in the film. This explains the mandible crevasse in his chest.
What Could Have Been: The original story was originally Godzilla fighting his predcessor in a form of a ghost (the 1954 Godzilla by the way), but the idea's been scrapped due to the idea of two of Godzilla's enemies being another Godzilla or Godzilla-like monster had already had its use. So now, they used the elements of the original film, and made out a monster born from the very weapon that killed the first Godzilla.
Anguirus was originally to be a part of this scrapped idea as a guest character.
Junior's resurrection was originally a stinger, but Toho felt no one would see the scene by the time the film was over. So it was put as a final scene.