Revealing mistake: When Buford is about to duel Marty, the back shots of Doc show his hair short, as opposed to the front shots, revealing it's a stand-in.
Sacha
Deliberate mistake: In the duel with Marty, when Tannen gets fancy spinning his gun, when he places it in the holster the grip is facing forward. They then use effects to turn the gun so the grip is facing back. (01:26:44)
Suggested correction: No, the gun is spinning on his finger and goes into the holster with the grip facing towards the back, which is completely consistent with the spin of the gun.
Visible crew/equipment: When Marty pulls over by Hilldale watch the car door by the lock: There's a man reflected, most surely a crew member who disappears in the opposite angle.
Revealing mistake: When Doc jumps from the horse to the train, right after he hurries Marty, the man on the horse is an obvious stunt double for Michael J. Fox.
Continuity mistake: When Marty holds the temperature-meter and warns Doc to put the yellow log inside the firebox, his finger suddenly disappears between shots.
Continuity mistake: When Buford hangs Marty, he puts the rope around his neck once. In the close-up the rope goes around twice.
Sacha Continuity mistake: When Marty and Buford duel, Seamus' distance to the bartender keeps increasing / decreasing randomly between shots.
Sacha Continuity mistake: When the train hits 70 mph the chimney explodes to pieces. When the bar that Clara holds onto breaks the chimney reappears.
Sacha Revealing mistake: When the train pushes the DeLorean and hits 70 mph Doc tries to grab Clara. In the wide shots (where we can't see his face) his coat whips, but in the close-ups where we do see his face the coat flutters, revealing that the train was going much faster with the stuntman.
Sacha Revealing mistake: At the festival, after Marty is given the gun he encounters Seamus and Maggie. Due to the Vistaglide camera effect where Marty was later added to the scene, she is unable to look at where Marty is supposed to be. This is very noticeable when Seamus says "buffoon" and Marty turns around and starts to walk, but Maggie keeps staring at where he was. Also when the scene ends and she looks at Marty and warns him to watch for the future, she's totally missing the spot.
Sacha Continuity mistake: After the festival, Marty wakes up and grabs the gun belt, which is missing a bullet. When he mimics in front of the mirror the bullet has magically appeared.
Sacha Continuity mistake: When Doc holds the telescope and tells Clara that he'll fix it, right when they date at the festival the position of the telescope changes between the front and back shots.
Sacha 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.
Sacha Continuity mistake: When Marty is about to duel against Buford he is inside a house peeping through the window, pulling the curtain open. The position of his hand and the opening of the curtain differs between shots.
Sacha Continuity mistake: Buford spills the spittoon on his shirt, but when he lassos Marty his shirt is dry and clean.
Sacha Continuity mistake: When dueling, Marty's holster belt on the floor changes positions between shots.
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.
Sacha 
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 skewed (and seemingly it must have a tap) and the liquid is falling out in large amounts to avoid the actor from drinking it.
Sacha Continuity mistake: Just when Marty parks inside the cave to hide from the Native Americans, one wearing a war bonnet jumps over the mount. When the angle changes, the man is gone and has been replaced by two riders with no war bonnets.
Sacha 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.
Sacha 
