Big Hero 6 hit theaters with a rocket-powered punch, thanks to superpowered nerds and a cuddly robot. People all over the net are going to try and take this apart piece-by-piece, and I can't speak for all of it, here're some pop culture (and especially Marvel Comics) nods you might not have caught. SPOILERS, naturally.
"Inspired By" not "Based On"
First and foremost, this movie is very loosely adapted from the American-produced Marvel comic series of the same name. Marvel isn't putting out any Big Hero 6 comics for the time being - apparently the film is different enough not to warrant it - but they are publishing an English translation of a Japanese-produced Big Hero 6 manga more closely related to the film.
Notable differences from the original comics include (but are not limited to): Hiro lives with his mom, not his aunt. Baymax was built with input from Hiro's deceased father, not a sibling. Wasabi-no-Ginger's powers are based on focusing his qi, not superscience. Fred is a member of Japan's aboriginal Ainu people raised on an American military base, not the slacker heir to a rich family. Et cetera, et cetera. That said, the transition works really well, and some stuff probably wouldn't have worked in a children's flick (like Baymax having the personality of Hiro's dead dad). There may or may not have been an allusion to the comics when a tough, patch-eyed woman appeared in the film's opening. A similar figure serves as the government liaison to Big Hero 6, a mysterious woman named Agent Furi.
The Man in the High Castle
The filmmakers were not necessarily thinking of Philip K. Dick's Hugo award-winning novel Man in the High Castle while making this film, but dang if it doesn't seem like the whole thing takes place in an alternate reality where Japan (and Axis) won WWII. In this alternate history, California is still has an ethnic and racial make up not too far removed from the real world US, but culture and language are dominated by the Japanese conquerors. Looking around San Fransokyo, there is a distinct lack of US flags (and in fact, some other, indistinct national flags are seen) and plenty of Japanese influences. Seems a lot more peaceable than Dick's novel - maybe international politics settled down by the present time?
Obviously, since the original comic is set in Japan and the film is set in San Fransokyo, there's a lot of Japanese pop culture referenced in the film, especially things that would appeal to fans' inner otaku. Canny viewers will notice references to classic manga Mazinger Z (particularly on the clock in Hiro's room and the rocket punch), the chibi-like SD Gundam and television mascot Domo (both noticeable in the closing credits)! The team's color-coded costumes are even a nod to Sentai hero TV shows (the basis of American Power Rangers). I'm sure bigger mangaphiles than myself can point out more references.
Disney Shout Outs
This film was put together by much of the team that put together Wreck it Ralph and Frozen, so naturally there's a lot of Disney callbacks. Many of these go by too quickly to see, but Frozen-villain Hans (the statue Baymax attacks) and minor characters from Disney's Bolt (a photo in the police station) can be seen in the background. Then there's that red dragon seen in several places (including both Hiro and Fred's rooms) - Jake Long maybe? Or possibly Grogg? There's plenty more Disney allusions if you can find them.
Fred is a Fan of Marvel Comics
Ah, now the big one: What all was in Fred's room? Fred - no doubt his full name is Fred Lee - is a big comic book geek, and has the money for one heck of a collection. While many of the toys, posters and comics Fred owned were made up for the film (even if they were inspired by specific sci-fi properties), the life-size costumes deserve particular attention.
Some have suggested Fred's mascot costume is Marvel monster hero Manphibian. It's possible, but not necessarily the case. It's just as likely Droom, a giant lizard that likes stomping on Marvel's version of Tokyo from time to time. EDIT: And if it is Droom, that red dragon seen in Hiro and Fred's rooms could be Grogg, a horned redish dragon that has also attacked Tokyo.
More definite is Black Talon, a chicken-themed necromancer (because of course he is) who has threatened the likes of She-Hulk and one-time Sorcerer Supreme Brother Voodoo. Deadpool thinks very highly of him.
Then there's Orka, a long time nemesis of Marvel's greatest hero/villain (according to me) Namor the Sub-Mariner. This guy is a powerhouse that could challenge the Thing, but he could take on the Hulk if he was in close proximity to actual Killer Whales (okay, it's a weird power). Despite a long career as a villain, he actually died trying to be a hero. Go fig.
It's kind of hard to tell, but one of the costumes sure seems like Sleepwalker, one of Marvel's big new characters from the early 1990s like Darkhawk and Slapstick and all of the other heroes who didn't really make a dent outside the 90s. Sleepy's actually pretty cool if you imagine he's the superhero version of Morpheus from Sandman. He's not, but you could imagine that.
You only see his boot in a few shots, but another character clearly represented is Torpedo. Or perhaps Turbo. This actually seems like something of a cursed suit at Marvel, but it keeps getting passed around. Inventor Michael Stivak designed the costume, but died in it, handing it off to a guy named Brock Jones who tried to be a hero only to die fighting aliens. It eventually ended up in the hands of teenager Mike Jeffries who was about as skilled with it as you'd expect a kid who finds a supersuit in his dad's attic to be, so he too, died using the armor (though he called himself Turbo). Then his good friend (just friends) Mickey Musahi took up the armor, using it in ways none of her predecessors considered. She's repeatedly tried to retire before the hero game kills her too, but she keeps getting drawn back in. Good luck, Mickey.
Anyway, there were a bunch more references and allusions in the film. What all did you catch?