Continuity: When Marty is being chased by the Libyans, a few times it cuts away to show the instrumentation in the car. The first time the odometer reads 33064.2 and the trip counter says 88.8; the second time it's goes back a little to 33061.8 and 86.4. A few seconds later we see it as he turns the corner, and it goes down again from 33,061.8 to 32,994.4, the trip counter has gone from 86.4 to 19. In fact it's a completely different set of instrumentation - the bottom of the needle's angled in some shots and flat in others.
Dr. Emmett Brown: This sucker's electrical. But I need a nuclear reaction to generate the 1.21 gigawatts of electricity I need.
Marty McFly: Doc, you don't just walk into a store and buy plutonium. Did you rip that off?
Dr. Emmett Brown: Shhhhhh. Of course. From a group of Libyan nationalists. They wanted me to build them a bomb, so I took their plutonium and in turn, gave them a shiny bomb-casing full of used pinball machine parts!
When Marty is playing back the Twin Pines Mall demonstration video for Doc, the camcorder tilts itself between shots, judging by the lens which sits higher above the TV set when Doc starts shouting, "1.21 gigawatts." See more...
At 1:15 am on October 26, 1985, a crowd of people showed up at the mall that was used as the Twin Pines/Lone Pine Mall for the movie, which had come out months before. They wanted to see if anything peculiar was going to happen. Nothing did. See more...
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Continuity: When Marty is writing the letter to Doc before he goes into the future, the word "disaster" is the only word in the last line. Yet when Doc shows Marty the letter when it has been all taped up, "terrible disaster" is the last line. Also, the handwritring in each letter is different (i.e. Marty's signature). They are two different letters.
Revealing: When Doc Brown loses his footing on the clock tower as it begins to toll, in the next shot, when he swings about towards the clock the thin black stunt cable attached to his waist, that leads around the neck of the statue, is visible. Do not confuse it with the thick silver electric cable Doc is holding.
Marty McFly: Let's see if you bastards can do 90.