Exiled from Continuity: When adapting Big Hero 6 from an obscure Marvel comic to a Disney animated movie, both Disney and Marvel mutually agreed to divorce Big Hero 6 from the Marvel Universe entirely. Not only does the movie not reference any Marvel elements, but Marvel exiled the team from the comics as well, to the point where Marvel has stated they'll never reprint the old comics. The team's last appearance in Marvel continuity was in 2012, when they appeared in the Spider-Man storyline Ends of the Earth. Whether the characters of Sunfire and Silver Samurai are exempt from this is yet to be seen, as they were excluded from the movie due to being X-Men characters, which 20th Century Fox (which wouldn't be brought by Disney for another few years) had exclusive film rights to.
Gogo's been given the nickname "Ryuko Matoi" due to similar character design. Another nickname is "Speedy Queen".
Big Hero 6 are known by the fans as "the dorks of San Fransokyo" and "Baby Hero Squad".
Honey has been nicknamed "Honey Bun" after fans saw her with her hair tied up. Another nickname is "Chemical Queen".
When onscreen and/or mentioned together, Hiro and Tadashi are referred to as "Hamabros".
Slaymax for the killer-bot version of the pudgy health care companion.
Tadashi is often affectionately called "Tada-nii", a portmanteau of his name and the Japanese word for "big brother".
Keep Circulating the Tapes: Marvel has said that they have no plans to reprint the comic series the movie was based on, so your only option is to track down old issues of it or get it digitally on comiXology.
Missing Trailer Scene: Many of the clips from trailers where Hiro is working on Baymax' red suit is gone from the actual film, notably the famous one where he makes Baymax strike an awesome pose only for the armor to pop right off. Neither do we see Baymax chasing the soccer ball.
Multiple Languages, Same Voice Actor: Genesis Rodriguez (who is of Cuban and Venezuelan descent) voices Honey Lemon in both the original English recording and the Latin American Spanish dub.
T. J. Miller improvised most of Fred's lines, which makes the "Fred's Angels" song even funnier in retrospect. This means a lot of the other characters' reactions were also improvised, like Wasabi saying, "Fred, I will lazer-hand you in the face!"
A lot of Maya Rudolph's facial expressions were copied for Cass, especially the faces she makes when talking about her extra-spicy hot wings.
Cass Hamada was initially shown with a tattoo on her forearm, before it was removed from the final film. Gogo would also have had tattoos.
Hiro's cat, Mochi, was also supposed to get an "upgrade" and join the team as Rocket Cat, but this was scrapped and instead used as a quick gag in the "nerd lab" scene.
Early concept art showed that Yokai had his own team of supervillains (including Mr. Yama and his goons). He also would eventually be consumed by microbots, which would take on his shape and act as the real villain.
Originally, GoGo was a very cynical character: She disliked Honey Lemon because she thought her fashions were due to boys, attention-seeking and did not approve of Hiro ordering her what to do when they formed Big Hero 6 because she always wanted to be number 1.
The 2013 Rotoscopers video and early information regarding the plot depicted Hiro with a slightly different backstory: He was already attending classes with Tadashi and could not fit in with the other students due to his intelligence (though he doesn't seem to mind). The Rotoscopers video also depicted Hiro as part of a "science club research team" lead by Tadashi (most likely consisting of Honey, GoGo, Wasabi, Fred) in which each individual would make different things and would eventually lead up to a competition. Like Tony Stark, Hiro felt pressure over using his intelligence for good or just building battle robots in the basement (garage in the final film). Also, in early stages of the story, Hiro was responsible for the creation of Baymax, as opposed to Tadashi, just like in the comic book. And the early plans for Wasabi was to make him the quiet, strict character with talent for being a sushi chef like in the comics. Cass was also originally planned to be Hiro and Tadashi's mother rather than their aunt.
Originally, Fred was going to use Hard Light holograms which he shaped into Kaiju, an homage to his ability in the comics where he could project an aura shaped like a giant monster.
Man of Action Studios actually wanted to revisit the characters with a cartoon, similarly to what they had recently did with M. Rex (which became Generator Rex). However, this is when they learned that Disney was already in development with a feature film. Man of Action had no creative involvement with either the film or the animated series that followed.
Word of God: Scott Watanabe confirmed that San Fransokyo is indeed San Francisco during an alternate future after the 1906 San Francisco Earthquake (retconned to the Great Catastrophe in The Series), rebuilt by Japanese immigrants using techniques that allowed movement and flexibility in a seismic event.