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.
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.
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.
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.
Continuity mistake: Buford spills the spittoon on his shirt, but when he lassos Marty his shirt is dry and clean.
Continuity mistake: When dueling, Marty's holster belt on the floor changes positions between shots.
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: When Buford duels Marty, the people behind him differ between shots. In the shot outside, there's a tall man with a blue shirt, a young guy and a man with a white shirt. From the angle shot inside the bar, the number of people behind the group has doubled, the man in white is gone and a woman has magically appeared standing next to the man with the blue shirt.
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: When Marty arrives at the bar the bartender lays both hands on the counter, the right one next to a bottle. When the angle changes, his right arm is up and the bottle is half a meter away. This changes back and forth depending on the angle.
Continuity mistake: Watch the guy at the back of Needles' car, the one holding a Pepsi can. The position of his right arm has no continuity in any shot.
Continuity mistake: When Marty is about to race against Needles, he spins around and his truck goes in reverse. Jennifer ducks, but a shot later, from a different angle, she is sitting tall.
Continuity mistake: When Marty drives Jen to the train wreck, she talks about her dream and the car comes to a stop. The position of Marty's hands on the wheel changes between shots.
Continuity mistake: After the modern train destroys the DeLorean, Marty lays on the grass, face down. Then, in a close-up, he turns around to watch the train. When the angle changes he is still facing down and crawling on the grass. In the following shot he has moved 5 meters to the right and is sitting by the bushes close to the tracks.
Continuity mistake: When the modern train is about to destroy the DeLorean, Marty exits the car jumping head first onto the ground. In the immediate next angle he has magically moved 4 meters to the left and is standing tall, jumping over the bushes towards the lawn.
Continuity mistake: Doc warns Marty to watch out for the "Track ends" sign which can be seen just 10 meters away. Despite that short distance, the action goes on for several seconds. Given their speed, they should have crashed almost immediately after Doc's warning.
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.
Continuity mistake: When Buford chases Marty, the position of his 3 goons is an absolute mess and changes from shot to shot with no continuity whatsoever: Sometimes they're behind Buford; or two riders on the right and one on the left; or last but not least: all three riding past Marty until a shot later one of them suddenly appears way behind the group.
Continuity mistake: When Buford chases Marty, note the second building after the bar, the Stetson house with a semicircle on the roof. Buford passes by this place at least three times during the chase.
Other mistake: After Mad Dog tries to kill Marty at the bar, a man says "you better run, squirrel." Marty is crouched, 4 meters away from the counter, but in half a second he has managed to stand up, run to the counter, jump on it and run towards Buford.
Answer: He simply has an absurdly low tolerance for alcohol, and whiskey is not a wise choice if this is the case. It helps set up the joke when Marty asks the bartender, "How many has he had?", and he replies by telling Marty, "Just the one", as we are meant to think Doc has been in the bar all night drinking away his sorrows.
Jazetopher