Continuity mistake: After the DeLorean with the dog in zooms in between Doc and Marty's legs, all of the angles show that there is no license plate anywhere around. Suddenly it appears spinning in front of them, as if it had been there all the time.
Continuity mistake: After Marty exits the cafe to make himself a skateboard out of two wooden crates, the crates are half a meter apart from each other, but close in the next angle. Also, the chubby kid holding his friend's crate swaps to holding his between one frame and the other.
Continuity mistake: After Marty is looking in awe at the 1950's records store, his hair swaps from messy to brushed backwards right when he walks backwards on the grass.
Continuity mistake: After Doc Brown sends Einstein one minute into the future, the rest of the scene until he returns is played out in real time. There are no scene cuts, and any camera angle changes are accompanies by continuous audio which negates any possibility that time has been stretched or compressed. However, it takes Einstein 1 minute 21 seconds to return.
Other mistake: When young George and Marty are in the backyard talking about what will happen at the dance, young George hangs up clothes to let them dry, but if you look closely the clothes are actually already dry.
Character mistake: Before playing Johnny B Goode Marty says it's a blues riff in B, but then plays the song in B-flat.
Continuity mistake: In the whole where When Biff is chasing Marty (on the 'skateboard') around the Town Square, the sun changes at every shot.
Continuity mistake: Before Lorraine brings Joey's cake, George leaves a bunch of crumbs on the table and starts to watch TV and do some numbers. After the cake lands on the table, the place is spotless.
Continuity mistake: When Doc syncs his stopwatch and the dog's, he holds them away from their bodies. A frame later his hands are close to his chest and there's dog hair all around.
Continuity mistake: After Joey's cake lands on the table, George puts his arm to the right of the cereal package. A frame later it's on the left side and holding a pencil.
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.
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.
Deliberate mistake: The sequence with the Libyans chasing Marty at the end of the film is much shorter than the original chase.
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: At the school when Marty is about to fight Biff, in the background there is food that changes position between shots.