Serendipity Writes the Plot: Hayter has mentioned in an interview that the reason why the dialogue had to be re-recorded for The Twin Snakes was because all the original dialogue was recorded in an apartment that had been converted into a recording studio. With the GameCube's much improved sound card, the player would have heard the traffic outside.
Throw It In: Gray Fox's presence as the Cyborg Ninja, not to mention the entire concept of the Cyborg Ninja, was not originally going to be in the game: Yoji Shinkawa suggested that they add in the concept because it seemed cool.
What Could Have Been: Hal Emmerich/Otacon's appearance was supposed to be more indicative of a combination of Dennis Nedry and Michael Moore (ie, an overweight slob with a baseball cap and always eating a chocolate bar). The design used in the final version was pitched in by Shinkawa as a way to rebel against it. Incidentally, this is why Otacon twists his ankle and has trouble hobbling around the base; his previous design was too out-of-shape to get any mileage.
Snake was envisioned by Kojima as being a lot older, clean-cut, and less hard-boiled then he ended up being. Again, it was Shinkawa who came up with his final design.
Decoy Octopus was supposed to have a boss fight, but it was scrapped due to them not being able to do what they wanted with it. Aspects of the fight were used in Metal Gear Solid 4 in the Laughing Octopus fight.