Revealing mistake: After the train destroys the DeLorean, its vanity plate is shown spinning around. Just like in the first film, the plate is attached to a steel post stuck into a hole in the train track, which is visible. (01:43:50)
Factual error: When Marty arrives in 1885, he's heading towards the Indians at over 70mph with only a matter of meters between them. In the next shot, Marty has stopped the car and is reversing. Even on asphalt, Marty would need the length of two Olympic swimming pools to stop the DeLorean from 70mph. It would be impossible for him to come to a complete stop given the distance he had.
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