Continuity mistake: When Doc and Marty get on the train at the end, Marty has some trouble getting on, and note that his hat falls off in the sequence, but in the next shot when Doc and Marty fall the hat is back on. (01:31:15)
Continuity mistake: When Doc and Marty are chasing the train, first their shadow is on the left of them, then in the next shot it's on the right. (01:30:40)
Continuity mistake: In the scene where Marty is driving the black Toyota pickup at the end of the movie, the truck's registration plate is missing - it can be seen when the truck is in the garage at the start of the film. Also the driver's door quarter light (vent window) is open. When we see the inside of the door it is closed. (01:41:45)
Visible crew/equipment: During the party scene, towards the end when Marty and Doc are discussing the duel and the fact the train may be late, you can briefly see a PA system center left of frame (bass cab with PA head on top and above it 2 tweeters side by side) it would make sense that a PA system be on set during the scenes so the band and dancers had a soundtrack to mime/dance to. (01:01:29)
Continuity mistake: Watch as Seamus hands Marty the baby, there is a definite "jump" and Marty is facing in almost completely the wrong direction, looking for a clue from the set's crew as to where he should be looking to catch the baby from... (00:24:20)
Revealing mistake: When Clara's dress rips off and is about to fall off the train, Doc saves her. One can notice it's not Christopher Lloyd but his stunt double. (01:41:17)
Continuity mistake: When Marty is about to race against Needles, he holds the wheel with both hands. An instant cut later, his hands are gone.
Continuity mistake: When the movie is about to end, Marty picks up Doc's photo. From the front shot he is grabbing it by the middle, but in the opposite angle he holds it by the lower end. (01:48:40)
Continuity mistake: When the movie ends, Marty and Jen are blown away. They're either landing on shadowy or sunny grass, depending on the angle. This changes back and forth. (01:49:05)
Continuity mistake: When Doc gives Marty the picture of them, Marty opens the package and leaves the wrapping paper behind. A shot later, from a a different angle, the paper is all around the picture.
Continuity mistake: After visiting Seamus, Marty walks to the Hill Valley train station where a man is by the ticket window. In the next shot the man has disappeared. (00:26:35)
Continuity mistake: At the bar Doc says that in the future people run for fun. When the guys playing poker laugh at him, the bartender magically appears next to them between shots. (01:17:43)
Continuity mistake: When Marty holds the baby, the gown covers his legs. In the close-up the gown is up and the legs are bare. (00:26:03)
Continuity mistake: When Doc passes out after drinking whiskey, he falls face down against a table and his back gets wet. When the angle changes it's dry and covered with glass.
Continuity mistake: After Doc meets Clara he and Marty watch a tombstone. Doc grabs the picture and says "my name has vanished!" The way he holds the picture differs between the first and second shot.
Continuity mistake: After the bartender prepares the wake-up juice, the two men by the table behind, plus the smoke coming out of the ashtray, disappear. When Marty pours the liquid the men reappear. (01:19:43)
Continuity mistake: After Clara pulls the emergency pull cord she jumps out of the train with her gloves on. From the immediate opposite angle her hands are bare. (01:26:04)
Continuity mistake: When the train hits 70 mph the chimney explodes to pieces. When the bar that Clara holds onto breaks the chimney reappears. (01:39:53)
Revealing mistake: When Marty pours the wake-up juice through the funnel into Doc's mouth, in the close-up the funnel is straight, but we can't see Doc. From a different angle where we do see the funnel stuck in his mouth, check the right side of the screen: The funnel is actually skewed (and seemingly it must have a tap) and the liquid is falling out in large amounts to prevent the actor from drinking it. (01:20:04)
Revealing mistake: When Clara horseback rides towards the train, when she reaches for the handlebar she is replaced by a very obvious stuntwoman who looks nothing like her.
Answer: Someone would go into his barn and do what? See a sign that says time machine and believe it and then use it? Seems highly unlikely.
lionhead