The Paradox script.
Despite the cliffhanger ending, there were originally no real plans for a Back to the Future sequel. However, once the studio became dead set on making one, director Robert Zemeckis and co-creator Bob Gale agreed to come back to make it. Conceived as a single sequel, a script called Paradox contained elements that were eventually split into II and III. Paradox remained the working title for the sequel shoots and parts of that script were used in the novelizations of the two movies.
An even earlier version of the sequel story, predating Paradox, saw Marty traveling back to the 1960s. He's arrested because he doesn't have a draft card. Lorraine bails him out and as a result she no longer has the money necessary to travel to San Francisco to meet George to celebrate their anniversary. As Doc says in that version of the script, this was supposed to be the night that the McFly parents, "Engage in biological reproductive mating behavior." Had producers stuck with this version of the sequel story, we most likely wouldn't have even visited the Old West.
As most fans know Back to the Future II and III were filmed back-to-back, a then relatively unprecedented move for a major movie studio. Doc Brown wears a shirt through the majority of the second movie with illustrations of trains and cowboys on horses: an awesome bit of foreshadowing for the events of Back to the Future III.
Fake Hill Valley, real lightening.
Back to the Future III was allowed to film in Sonora, California rent-free under one condition: they had to agree to leave all of those cool Old West buildings there, in hopes that the sets would serve as an attraction for other Western themed productions to come and film there. Universal Studios agreed, taking only the Clock Tower when they left. The county itself served as the site for Gary Cooper's For Whom the Bell Tolls, Gregory Peck's The Big Country, Clint Eastwood's Unforgiven, and TV shows like The Lone Ranger, Rawhide, Gunsmoke, Bonanza, and Little House on the Prairie. Six years after the release of Back to the Future III, the movie sets sadly burned down, in a 7000-acre fire started, like many fires, by a bolt of lightning.
The Clint Eastwood joke.
Speaking of Clint Eastwood, there's a great Clint Eastwood joke at the drive-in theater. (Doc replies: "Who?") But even better, there's a subtle visual gag involving Eastwood, as well. As Marty emerges from the bathroom in his cowboy getup, two of the posters on the wall are from b-movies that featured a then-unknown Eastwood.