Continuity mistake: While Marty is at Lou's Cafe, Biff and his gang enter. When Biff starts bullying George, note George's haircut with shaved sides, back (above his neck), and sideburns. In the following shots, George's haircut with its shaved areas change length. This happens again, when George is with Marty and then tries to ask Lorraine to the dance. (00:39:00)
Continuity mistake: Throughout most of the film, the licence plate on Doc's car reads 8N 39742, but after the DeLorean travels back to 1985, it changes to 7F 42857. (01:41:31)
Other mistake: The car that almost runs Marty over has the vehicle registration plate of 6S 48405. Later on, when Marty is hit by Sam, Sam's car has the same plate. (00:35:49 - 00:42:02)
Factual error: When Marty hits his head on the DeLorean's steering wheel, the car's horn honks. This is inaccurate to the design of real-world DeLoreans, as a DMC-12's horn button is actually located at the end of the turn signal lever rather than in the steering wheel. (01:39:27)
Suggested correction: You can't see his left hand and he could have accidentally pushed it when he hit his head. Or Dr. Bown customized the steering wheel so the horn is in it, like he customized the entire interior of the car.
I thought the point was that the car was so unreliable that when hit his head on the steering wheel, the horn went on. Makes sense to me. I own a DeLorean by the way.
Continuity mistake: When the Libyan terrorists show up in the VW bus, there is no license plate at the front, but in some of the following shots during the scene a blue license plate is affixed to the front bumper. (00:28:55)
Revealing mistake: When the DeLorean is about to time travel for the first time, the fuel trails to achieve the following fire trails are already visible on the pavement. (00:22:00)
Factual error: Video/audio output on the JVC camcorder (if it had any at all) would not be compatible with 1955 TV. if available the camcorder output would be composite, component or COAX - all would need some sort of adapter for the audio/video to work on the TV. COAX would be the simplest, but they would need to invent the 75 ohm to 300 ohm adapter.
Factual error: In the skateboard chase scene, after the crash, a crowd gathers. In this crowd there is a kid dressed in a Cub Scout uniform. He has a red/white town strip patch on his arm. In 1955 the Cub Scout town strip patches were blue with gold lettering. (01:07:48)
Continuity mistake: When Biff's gang arrives at the diner for the first time, Skinhead walks behind Marty and plays with a ball. When the shot changes, he is walking behind him again, but this time he is not toying with the ball. (00:38:50)
Continuity mistake: When Marty tells George how to flirt with Lorraine, they both enter the diner and Marty sits on the back of the counter but disappears between shots, only to reappear later on. Also, the extras around him change, although they're all dressed in similarly colored clothes. Check a man in a plaid jacket next to the blonde girl in pink, who disappears when Marty trips Biff. This continuity havoc was due to the combination of Eric Stoltz scenes and new Michael J. Fox reshoots.
Continuity mistake: When young George walks to Lorraine's table to read the poetic lines, the pen in front of her books moves suddenly to being on the right side of the books. (01:04:42)
Continuity mistake: When Marty enters Lou's Cafe for the first time, check a group of people gathered outside next to the doors who say goodbye and leave the place. A shot later, they're all back together, talking. (00:37:46)
Continuity mistake: At the very end of "Earth Angel", after kissing Lorraine, George waves to Marty on stage, who waves back and flexes his right hand, holding it up. It then switches to a wide shot for the end of the song, and Marty's right hand is down on the guitar again.
Continuity mistake: When Marty is holding on to the back of the truck, Biff attempts to hit him with his car. Marty quickly pulls himself to the side of the truck to avoid being hit but in the next shot, he is holding on to the back of the truck.
Character mistake: At the beginning of the movie Marty is turning on a huge guitar amplifier. The two switches for the filaments are misspelled. They are shown as "filiment." (00:03:25)
Continuity mistake: Some of the items in Doc's lab change position between the shots of Marty standing in front of the amplifier and it exploding. (00:04:15)
Continuity mistake: When Marty looks at the car he is about to crash into, there is no one standing on the pavement, but when he jumps onto it, a man appears. There was not enough time for him to appear. (01:07:00)
Continuity mistake: When Doc takes the photo from Marty, the way he holds it changes between shots. (00:50:07)
Revealing mistake: When Marty begins to slump down due to fading from existence look at the guy playing the piano behind Marty, he's not even pressing the keys on the piano just putting his palms on them repeatedly.
Visible crew/equipment: When Marty asks if the time machine is nuclear, a boom microphone is visible in the right windows of Doc's van. (00:26:28)
