Not in the series itself, but in Super Smash Bros. Brawl, if using the Codec when fighting Captain Falcon at Shadow Moses, Otacon and Snake will reveal that they are both fans of the character. In the Japanese version of F-Zero's anime adaptation (Falcon Densetsu), Captain Falcon is voiced by Hideyuki Tanaka, who voices Otacon here.
In The Twin Snakes, Rob Paulsen provided the voice of Gray Fox instead of Greg Eagles. Eagles would reprise his role as Donald Anderson, however.
In an interesting case, both Eagles and Paulsen did not reprise their roles for the Digital Graphic Novel. Anderson and Gray Fox were instead voiced by James C. Mathis III and Larc Spies, who respectively voiced these characters' younger selves in Metal Gear Solid 3 and Portable Ops.
Recursive Import: The Japanese Integral edition has English voice acting and all the other added content from the overseas releases (multiple difficulties, Snake's tuxedo costume), in addition to having its own exclusive content (a sneaking suit for Meryl, a new weapon, new Codec frequencies and a first-person play mode).
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.
Because of some ambiguity about union rules regarding video game productions, most of the English cast used pseudonyms for the first game, with only David Hayter, Doug Stone, and Scott Dolph receiving credit under their own names. With later games, this was no longer an issue, so the returning actors' real names are credited in The Twin Snakes.
Hayter was originally credited as "Sean Barker" in the demo; he received SAG's blessing in time to get his real name in the game. Stone, who used Stage Names for some of his other work, had previously recorded for video games under his own name, while Dolph was a Konami production staff member who simply provided some extra Genome Soldier lines.
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.
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 technical limitations on the Playstation hardware resulting in the concept for the fight being impossible to achieve. Aspects of the fight were used in Metal Gear Solid 4 in the Laughing Octopus fight.
Psycho Mantis was originally going to reference games that were developed by other companies as well. This wasn't included because Kojima couldn't work out any deals with said companies.
Ryuhei Kitamura originally wanted The Twin Snakes to have faithful recreations of the original cutscenes, but Kojima requested that they be made more over-the-top due to his admiration for the former's cinematic style.
Gray Fox/Frank Jaeger wasn't even originally going to be in the game. The Cyborg Ninja was a completely unrelated sketch Shinkawa had drawn in his spare time. When Kojima first saw the drawing, he was so impressed by the design that he felt it would be a waste to not use it in the final product, leading him to rewrite the script and giving Gray Fox a prominent role in the story.
The ability to hide bodies in lockers was planned for this game, but technical limitations meant it had to wait until Metal Gear Solid 2: Sons of Liberty. Another feature that had to wait another game to be realized was Solid Snake's bandana tails - files can be found within the game's data that they were intended to be present and animated here, but once again technical limitations forced it to be cut.