God Never Said That: For a long time it was shown on the movie's poster that Gigan could fire an Eye Beam from his forehead, above his eye, yet this ability was never shown in the film. Many fans speculate that this was due to budget reasons, evident by the abundant amount of Stock Footage in the film. It was later reveal however by Special Effects Director, Teruyoshi Nakano that the REAL reason it was never shown was because he didn't believe it fit with the character, so neither film demonstrated this ability for said reason. This all can be read here.
Additionally, Gigan also possesses the ability to breathfire, but was never shown to in the film for the same reason as above.
The first idea had Godzilla and Anguirus "team up" with a Rock Monster named "Majin Tuol" to fight Ghidorah, Gigan, and Megalon. Other differences that were to take place was that Godzilla Tower was just a base of operations for the heroes, the villainous leader behind the monster attacks was a floating brain named "Alien Miko", and Majin Tuol's only existence was to kill the Space Monsters (with the exception of Miko, who is killed by Godzilla).
The second idea had Godzilla team up with Rodan and Varan to fight Ghidorah, Gigan, and a Dragon Monster named "Mogu". This idea was much more closer to the film that it is today, introducing the villainous Space Hunter Nebula-M aliens, as well as the monsters being summoned by tapes being played. The film also was to focus heavily on King Ghidorah, hence it's original title as "The Return of King Ghidorah". The idea was eventually dropped with the budget of making new suits for Rodan, Varan, and Mogu was too expensive and instead were substituted for Anguirus. This idea also was to give Gigan a Mace for one of his hands.