An ongoing gag from all three movies is the unfortunate way that Biff (and Mad Dog) keeps ending up in manure. All three movies feature a scene of this kind, and the version from the third film even features an additional easter egg.
In the first two films, it’s due to vehicular misadventures that land the bad guy in the bad stuff, but in “Part III” it’s because of Marty’s heroic gunfight and fistfight with Mad Dog. When Marty lands the knockout hit, Mad Dog spins and passes out just like Biff did when George McFly punched him near the end of “Back to the Future”.
Near-Deadly Consequences
Plenty of accidents happen on set, but most of them are simple trips or flubs. In "Back to the Future Part III", however, something much worse almost happened. At one point Marty is dragged behind a horse and hanged.
Because Michael J. Fox wasn't standing on a box – his own choice in order to make it more realistic – after a few takes he got tired and couldn't get his hand under the noose in the right spot to keep his airway open. He actually passed out for a few seconds before the filmmakers noticed. He later recounted the incident in his autobiography "Lucky Man".
Switching Things Up
After two full films, we've gotten used to the catchphrases of the two main characters. Marty McFly calls things heavy – a very eighties phrase – and Doc Brown likes to exclaim “Great Scott!” By the time we get to the third film, the characters and the filmmakers decided to swap things around.
The characters have at this point become so close that, after one shocking scene, Marty yells out “Great Scott!” immediately followed by Doc Brown saying: “I know, this is heavy.” After two whole films of establishing the characters, it's fun to see them swap phrases for a one-off joke.
The Shirt's Second Appearance
It's hard to tell, but one scene in "Back to the Future Part III" has a unique throwback from "Part II". At one point, Doc Brown and Marty put on their best wild west bandit looks with cowboy hats, dusters, and bandannas.
If you look closely, you can see that Doc's bandanna is made of the same material as the Hawaiian shirt – the one with men on horseback chasing the train – from "Part II". Writer Bob Gale said it was the same fabric, but faded and washed out so much it might have been impossible to tell if he hadn't pointed it out.
Not a Real Train
In the climax of the third film, Doc Brown, Marty, and Doc Brown's lady Clara Clayton (Mary Steenburgen) have to drive a train into a canyon in order to reach the requisite speed required to get Marty back to 1985 with all problems finally corrected.
While it might have been pretty cool to send an entire steam locomotive shooting into a canyon in what must only result in a huge explosion, it's just not feasible. For both economical and shooting reasons, the filmmakers went with a model that topped out at about fourth the size of a real train.