Para-Medic calls Snake "a real Captain Nemo" after he states that his name is John Doe. Akio Ohtsuka, the Japanese voice actor of Snake, had previously voiced Captain Nemo in the anime series, Nadia: The Secret of Blue Water.
And furthermore, for the Japanese version of the game at least, the comical Non-Standard Game Over messages from Colonel Campbell (when he berates you for creating a Time Paradox via killing Ocelot, EVA or Sokolov) is an allusion to Takeshi Aono voicing Doc Emmett Brown in the Japanese dub of the Back to the Future movies.
There's also plenty of made up plants and animals: For example, there's no such thing as a Baltic Hornet (hornets can't make honey) and there is no golova fruit (although, it's based off of a real fruit called a jackfruit).
Artistic License - Geography: Good luck finding any tropical jungles anywhere in the former Soviet Union, not to mention the ludicrous variety of animals housed in it. The justification is that the animals were brought into the jungle from other regions by the scientists for research purposes, and the jungle setting is there mostly to trick people playing the pre-release demo.
Despite the game saying it's a "jungle", it looks more like what's called a mixed forest, which the Soviet Union did have, for instance the Caspian Hyrcanian zone in Azerbaijan. Also, there actually are pockets of lush forest right next to arid mountain regions in areas of Tajikistan (where the game is suggested to take place) like the Varzob region. The mountainous areas later in the game also resemble the lower ranges of the Tian Shan mountains in Krygyzistan.
Artistic License - Economics: The Philosophers' Legacy consists of enough money to fight the Second World War five times over. The economic repercussions of putting this much money aside and doing little with it, then losing it, although the next game actually does deal with the economic repercussions somewhat.
Creator Backlash: Done to Raiden from the previous game. Zero devotes a long CALL to the fact that the Raiden mask irritates him, and the Raiden mask is used to pose as Raikov, the impulsive, despised and ill-tempered lover of everyone's favourite homicidal lunatic Volgin; Snake beats him up and hides him in a locker, with the option of actually killing him. This pleased Raiden's substantial Hatedom to no end. He got better.
In the Secret Theater video Metal Gear Raiden: Snake Eraser, Raiden goes back in time to assassinate Naked Snake/Big Boss and take the Main Character Chair for himself. He ends up, among other things, getting kicked in the face by Naked Snake during the HALO jump, and is almost raped by Volgin, mistaking Raiden for Raikov.
The Metal Gear Solid 4 trailer also takes a potshot at Raiden, with the crowd booing heavily when he unmasks himself and his getting royally creamed by Snake during their fight for the main character chair.
Seems like after he reunited the two worlds, LloydIrving defected to the Soviet Union and became an Ocelot soldier, a scientist and a radio operator who calls off the MiGs at the end.
Life Imitates Art: ADAM is introduced during the Snake Eater briefing as an NSA technician who fled to Russia. Edward Snowden, anyone?
Screwed by the Lawyers: Why the Snake vs. Monkey minigame isn't in the 3DS and HD versions. Sony Computer Entertainment created, and owns the rights to Ape Escape, killing any chance the minigame has of being on other consoles by default (though that doesn't quite explain its absence in the PlayStation 3 and Vita versions).
Throw It In: Kojima wanted to use a piece of licensed music for the closing credits, and a colleague of his suggested he listen to the band stellastarr*. He misheard this as "Starsailor", and liked the track "Way to Fall", which ended up being used.
Related to the above, the credits theme was originally planned to be David Bowie's "Space Oddity" and "Ashes to Ashes" when space development was originally one of the game's main themes.
As the player goes through the game, Snake's injuries were supposed to leave visible scars on him, but the PlayStation 2's hardware capabilities were unable to handle this feature.
During the torture sequence, there was going to be various button prompts that would have Snake struggle and swear, but the concept was ultimately cut.
Kojima and Akio Ohtsuka proposed the idea of having the game be voiced in Russian. By the Japanese voice cast. Ohtsuka was so enthusiastic about the idea, he went for Russian lessons. The rest of the cast shot them down.
The Naked Sample tech demo for the 3DS showcased some significantly improved graphics, an updated sneaking suit design, and new set-pieces showing off the 3D capabilities of the 3DS hardware. Unfortunately, the actual Snake Eater 3D is more of a straight port with updated textures and added game mechanics from Metal Gear Solid 4 and Peace Walker.