Continuity mistake: When Marty rides off after borrowing the skateboard, a woman in the background bends over towards the end of the shot, but in the next shot, she is standing upright. (01:06:10)
Continuity mistake: When George is in the school cafeteria talking to Marty about science fiction stories, he holds the notepad differently with each changing shot. (00:58:55)
Continuity mistake: While Marty's 1950s family is having dinner, the milk bottle's level is one mark below the red printed label. A second later it's 5 centimeters above the red mark.
Continuity mistake: When Doc puts Einstein in the car, the dog turns his head inside the car. A frame later, from a new angle, it's outside the car.
Continuity mistake: When Marty was recording, Doc never hesitated between "reaction" and "to", then when they are watching the tape, he hesitates a little.
Other mistake: Just before Marty starts playing Johnny B Goode on stage, he tells the band members to watch for changes and other guidance advice to start the song. When the song starts, ALL the band members (who have never heard this song before) suddenly play all the chord changes perfectly and even the drums are perfect like the real song. In reality, never hearing that song before, the band would not have had this song perfected like that - every note and instrument sound.
Suggested correction: This is, of course, done intentionally to make the song sound like it actually is. It's highly unlikely but not impossible that these musicians put it all together just as the actual song sounds. You also have to keep in mind that the idea is given that Chuck Berry came up with the song hearing it through the telephone, so that's why the actual song sounds the same, as he is just mimicking what he heard.
Besides which, if this posting were valid, every movie musical in history would be riddled with similar errors.
Continuity mistake: When Goldy (or Golby?) says, "Mayooorr", George is facing Marty. Then when Goldy starts saying, "Now that's a good idea," George is facing Goldy, without any motion of turning. (00:40:35)
Continuity mistake: When Doc and Marty are watching the DeLorean burn out from across the vacant Twin Pines Mall parking lot, the radio control unit's antenna is seen lowered one shot then fully raised in the next, despite Doc not having touched it. (00:21:20)
Continuity mistake: When Marty sees the Lyon Estate works there's a mild breeze blowing. Just a frame later, from a new angle, there's a very strong wind. (00:34:18)
Continuity mistake: The time machine is gone for 1 minute and 21 seconds - not just 1 minute. (00:22:00 - 00:23:20)
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.
Continuity mistake: George's hair fixes itself when he tells Marty about Darth Vader coming down to visit him. It's initially messier.
Continuity mistake: Before Marty kicks the speaker while playing Johnny B Goode, there is a case of Pepsi below it which disappears between shots.
Continuity mistake: When Doc and Marty are looking for his dad at school, you can see a girl with a blue sweater going downstairs twice. (00:56:49)
Continuity mistake: When Marty stops the Delorean in front of the Lyon Estates sign after escaping the farm, notice the sun - it's overcast and kind of foggy. When he looks at the sign from another angle, it has become more sunny, and later in the day. When the couple with the car passes, it has returned to the same as before.
Continuity mistake: When Marty confronts George as "Darth Vader", after George asks "who are you?" Marty plays the music again, and George presses his hands to his ears. In the shot from behind, his hands are cupped around his ears, in a very different position. Then when Marty says "silence earthling", in the shot from the front his hand is away from his ear entirely. (01:02:35)
Continuity mistake: After George knocks Biff behind Marty there is a couple running to George, but in the open view they disappear.
Continuity mistake: When George is checking the time at the prom there is a girl in grey behind him that changes to one in pink. (01:18:56)
Continuity mistake: After Marty gets to the square in 1955 his hair changes after he grabs the newspaper.