Dawson Casting: Marty, Lorraine, George, Biff, Jennifer, etc. Makes some sense in Lorraine, George, and Biff's cases, since in the first movie they had to play both their teenage selves and their adult selves. Initially, not so much the case with Jennifer, who was played by 19-year old Claudia Wells in the first film, but then played by 26-year old Elizabeth Shue in the Sequels and that wig she wore to make her resemble Lea Thompson made her look every bit her age.
Disowned Adaptation: Bob Gale hated many of the video game adaptations of the franchise, particularly the first one by LJN Toys. According to him, the makers of the game didn't want any input from the filmmakers, and when he saw it, he wanted a lot changed, but was told it was too late to do anything. He advised fans not to buy it, and felt that Telltale Games handled the process much better.
Executive Meddling: Basically, this is the whole reason why the sequels exist in the first place — but Sid Sheinberg had insisted on certain changes to be made in the first movie.
One of Sid Sheinberg's changes, from "Professor Brown" to "Doc Brown" has become integral in Back to the Future culture. (Just how much so is suggested by Michael J. Fox's repeated bloopers in filming The Frighteners: he called the Judge character "Doc".)
Cost considerations forced a complete change in the tactic to return to 1985 in Part I, from powered by a nuclear test explosion to powered by the lightning bolt. By all accounts, it was a major improvement.
The Other Darrin: Elisabeth Shue replaced Claudia Wells as Jennifer Parker in the sequels. And Jeffrey Weissman takes the part of George McFly.
The Red Stapler: The DeLorean. At the time the movie came out the Delorean Motor Company had been bankrupt for almost 3 years and DeLoreans were considered a failed car. Nowadays there's an active "time machine conversion" community, DeLorean dealers, and DeLorean conventions — all because of Back to the Future. There's apparently even a company in Texas that bought the rights to the design and is making new DeLoreans.
Urban Legend of Zelda: Once real-life history got into the decade of the 2010s, pretty much every year there would be a picture claiming that that day was the day Marty went to when he went to the future (with the date being photoshopped to the current date). It's easy to tell the fakes, since the real years in the movies all end in 5. Only time will tell if these fakes will stop being made after the real date passes.
The first movie
The Cast Showoff: Kind of. Although Michael J. Fox is miming his performance of "Johnny B. Goode" he did actually learn to play the song (having played guitar in high school) so he could do so accurately.
Dummied Out: The scene where Marty, dressed in the hazmat suit as "Darth Vader", threatens George into taking Lorraine out to the dance was originally much longer. However, it was cut when the director realized that, since, in the next scene, George tells Marty what "Darth Vader" told him, it really just goes over the same information again.
The whole scene be found on Blu-ray and DVD releases, as well as here.
The head judge of the band contest is Huey Lewis (of Huey Lewis and the News), who also made the series theme songs Back in Time and The Power of Love (which Marty and his band are playing for the contest).
Non-Singing Voice: Michael J. Fox did not sing "Johnny B. Goode", although he did learn to play it so he could "mime" the guitar.
The Other Marty: Eric Stoltz was cast as Marty, and filmed some scenes, before being replaced by Michael J. Fox. You'll get to see some Stoltz footage in the Blu-Ray release of the Back to the Future trilogy.
Throw It In: Many of George McFly's mannerisms (the shaking hands, the infamous Honeymooner's laugh) were ad libbed by Crispin Glover.
Troubled Production: Everyone involved in the first film was sure it would bomb because absolutely nothing went smoothly. (Among the crew, it was nicknamed The Film That Would Not Wrap.) The shoot nearly drove Zemeckis insane, ruined his health, and threatened to wreck his career if the film wasn't a hit. Star Michael J. Fox was running on fumes, commuting between the BttF and Family Ties sets with virtually no sleep in-between. In his interview on Inside the Actor's Studio, he notes that he was basically a zombie, which luckily enhanced his acting a fair bit.
The original time machine was a modified refrigerator, changed because it would have been a very stationary prop and Steven Spielberg had images of children locking themselves in the fridge to the horror of their parents. They also would have driven into the blast of a nuclear bomb to fuel the flux capacitor, changed because that alone would have doubled the production costs and the clock tower lightning strike made a fairly simple and stationary location. In the script written for this kind of time machine, the original timeline's Biff became a cop that kept "borrowing" stuff from George and had a daughter. With the change in the timeline, Biff became a security guard working for George, who became a boxing champion in that script.
For younger readers who don't understand how someone could become trapped in a refrigerator, they used to be held closed with a physical catch that could only be opened by a handle on the outside, and these older models were still somewhat plentiful at the time of the film. Modern ones all use magnets to hold themselves closed, with no catches.
Eric Stoltz was originally cast as Marty; apparently only stills and a few clips exist of his work on the movie except for one scene that made it into the final cut — Stoltz running away from the terrorist van, entirely covered in a radiation suit. When initially casting Marty, the producers narrowed it down to two choices: Stoltz and C. Thomas Howell. Michael J. Fox was always their first choice, but the producer of Family Ties initially didn't want Fox gone from the show during Meredith Baxter's pregnancy. Zemeckis and Gale preferred Howell, but the executives preferred Stoltz, so Stoltz was cast. However, the execs told the Bobs that if Stoltz didn't work out, then they could go back and reshoot with another actor. Except no-one expected it to actually happen...
Also, John Lithgow was considered for the part of Doc Brown. In fact, Lloyd was ready to pass on the film, but his wife insisted the script was better than it looked.
Jeff Goldblum was another consideration for the role of Doc Brown.
Melora Hardin (who would later play Jan on The Office (US)) was originally cast as Jennifer to play opposite Eric Stoltz's Marty. However, Melora never filmed any scenes, and was fired after Marty was recast because she was a lot taller than Michael J. Fox.
After returning to 2015 from 1955, Biff not only walks away in inexplicable pain, but falls to the ground and vanishes.
Marty encounters Hill Valley High School, burnt down and fenced off from the rest of the town.
Marty meets his brother, now an alcoholic bum. Had their sister's actress not been pregnant at the time of filming, Marty would have met her as a prostitute.
Gone Horribly Wrong: The end of the hoverboard chase, in which Griff's gang crashes through the Courthouse Mall, nearly ended in the death of the girl's stunt-double when she crashed into the hard stone instead of the stunt-glass. This was the take they used in the movie.
"I've got something for you... a letter, ya jackass!"
Hey, It's That Voice!: Charles Fleischer, who provided the voice of Roger Rabbit, plays Terry, the mechanic who fixes Biff's car in 1955 and becomes the old man who asks Marty to save the clock tower in 2015. On the same note, in the shop where Marty buys the Almanac, there's a Roger Rabbit doll. Who Framed Roger Rabbit and the Back to the Future trilogy were both produced by Amblin, directed by Zemeckis, and starred Christopher Lloyd.
Flying cars? How about hoverboards? People were practically frothing at the mouth for those back when the film came out, not at all helped by Zemeckis' tongue-in-cheek claim that they were real. Made by Mattel, no less.
Potentially averted in some minor respects however:
A reference is made to books no longer being made of paper (predicting the rise of e-books).
1980s nostalgia is pretty strong in the 2010s.
Some of the jargon used by Marty and Jennifer's kids isn't too far removed from today's youth.
Marty's son is shown watching multiple TV channels at once, reflected in today's multitasking youth culture.
One joke in the film is the advent of the Scenery Channel. Such channels exist today.
Marty is fired due to his boss monitoring his actions; such privacy concerns exist today.
Sorta. Miami didn't have a pro baseball team when the film was made; they do now. However, it's not in the right league. The Marlins and the Cubs are both in the National League, so they could never compete in the World Series against each other. Plus, the Miami team in the movie had a gator logo, which doesn't fit either Miami's (Marlins) or Tampa Bay's (Rays) teams.
There was actually a chance of this happening. Before 2013, the National League had 16 teams while the American League only had 14. MLB wanted to move a team from the NL to the AL to have each league with 15 teams, and the Marlins were one of the candidates to move leagues (with not-insignificant support by fans just because of this movie, no less!) Ultimately averted, though - the Houston Astros were picked to move.
In a much more subtle example, the Elijah Wood kid complaining about having to use your hands on the arcade machine. Guess what Microsoft made recently that brought about hands-free gaming...
Movie-2015 has blockbuster 3-D movies. Guess what started becoming popular again in the real-world 2010s?
The woman at the curio shop mentions that the sports almanac is from the days where books were still made with paper. Is everyone in 2015 running around with Kindles or Nooks?
A poster in the back-alley advertises "SURF VIETNAM". This was a gag, at the time, but it is now possible to go on vacation in Vietnam, which actively courts foreign tourists.
Prop Recycling: All of the futuristic cars were recycled from other films.
Real Life Writes the Plot: The concept of an altered "bad present" where George McFly was murdered came about due to Crispin Glover's refusal to take part in the sequel. In spite of this, Robert Zemeckis cited II as his favorite of all the films he's made (and certainly the strangest).
Shrug of God: Bob Gale admitted in the DVD commentary that he has no idea what "lithium mode" is, and he doesn't know what illicit activities Future!Marty was getting into with the card scan.
According to Bob Gale, ideas proposed for Part II included a visit to Doc's family (with Christopher Lloyd playing his mother), and going to the days of Prohibition when Biff's ancestor was a bootlegger. The last bit was retaken for the first episode of the video game. And yes, Bob Gale worked on it.
The sequel originally had Doc and Marty going back to the '60s after Biff's interference and seeing Marty's parents as pseudo-hippies, and part of his goal would have been to ensure that he is conceived. About mid-way through writing this part, they realized that there was nothing really stopping them from revisiting the events of the first movie. In that version, George was already dead in 2015 (and it was NOT 2015-A). It was mentioned that, at some undisclosed moment, George's life had been saved at a hospital that had previously survived an attempt from the town to demolish it. In the timeline where Biff became wealthy, the hospital had been demolished. You can read about this version and its associated tropes on this very Wiki.
The sequel was originally a deconstruction of the first movie. Future Marty is a wreck because he's addicted to taking chances and trying to cheat his way to fortune. When the present day Marty discovers that he will turn out poor, he decides to secure his own financial future by buying the Sports Almanac. Even after seeing what kind of damage careless time travel can do in 1985-A, Marty still finds it hard to let go of the Almanac. Ultimately, the lesson he learns is that the best way to get a good future is to live a good life. Major parts of the story remain in the final movie, but the Aesop got muddled in rewrites.
If you look at the tombstone of George McFly in Bad 1985 and do a little math, Marty would have been just five-years-old at the time of his death. You can understand Biff being sceptical when Marty brings it up as an explanation, remembering from that age.
Fatal Method Acting: So narrowly averted by Michael J. Fox. While shooting the scene where he gets hanged, his hand slipped and he actually got hanged. Fortunately, a crewmember noticed he wasn't breathing and he got resuscitated.
The band at the town hoedown was ZZ Top, complete with signature spinning instruments.
Averted, but worth mention: President Ronald Reagan was a big enough fan of the series to reference the Flying Car future of Part II in his speeches, and of course was a veteran actor himself. He purportedly wished he could have played the mayor of the 1885 Hill Valley, and it was even seriously considered at one point. It's to the detriment of film history that it didn't happen.
Hey, It's That Voice!: People who've seen The Aristocats might be able to pick up the voice of Napoleon the dog as one of the bar patrons who heartily dismiss Doc's truthful claims about the future to be nothing more than the ramblings of a drunken lunatic.
So My Kids Can Watch: Mary Steenburgen played Clara Clayton in Part III (and subsequently in the animated series) because her children begged her. This was quite fortunate for the filmmakers, who regarded her as their first and only choice for the part.
The story of the game is based on the unfinished fourth movie script; and expanded on a fair bit. According to Telltale Games they revived the script, expanded it, and apparently had enough to actually fill up a fifth movie by Episode 4 & 5!
Biff's daughter Tiff was originally going to appear in Episode 3, but with Punk Jennifer there it was decided she was redundant.
There were plans to give Doc and Edna a kid, but they decided against it, due to the ethical ramifications of erasing a person from the timestream.