Factual error: Though extremely modest on today's standards, the dress worn by Clara to the hoedown shows far too much cleavage for the time. No schoolteacher would ever wear a dress like that in the 1880s.
Factual error: When Marty goes to meet Mad Dog Tannen for the duel, in the background on the right side is the current flag of California. But that flag did not become the state flag of California until 1911, so would not have been around in 1885.
Factual error: Standard gauge for railroad tracks in 1885 was 4ft 8 1/2 inches. The distance between the center of the wheels on a Delorean was 5ft 3 inches. The car would not fit on to the tracks, and we can see the wheels aren't recessed or otherwise altered.
Other mistake: When the movie ends and Doc says, "It means your future hasn't been written yet," watch his son Verne behind. He looks towards the camera and seems unhappy, makes a beckoning gesture (presumably at the crew), and points at his crotch. Seemingly, the kid was having a hard time trying not to pee on himself. (01:50:39)
Visible crew/equipment: At the drive in theater, Marty says he'll put the boots on when he gets there. The camera pans to the left to follow Marty and Doc as they continue to talk. On the very far left side of the screen, the shadow of the boom mic briefly dips into frame. This happens just before Doc walks over to the DeLorean from his car. (00:16:35)
Continuity mistake: When McFly gets to the village in 1885, he walks beside the manure guy and the sun changes between shots.
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: When Marty is about to race against Needles, he holds the wheel with both hands. An instant cut later, his hands are gone.
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 Clara is about to leave Doc's workshop, the position of Doc's hand on the telescope alters each time we move from rear to front shot. (01:08:09)
Factual error: Preparing to run the model train in Doc's workshop, Marty connects the clamp to the positive terminal. But he actually connects to the white ceramic insulator. Doc correctly connects to the negative metal terminal. (01:10:01)
Continuity mistake: While Marty is outside the mine, the sun changes on the floor.
Continuity mistake: When Marty walks around the old town and watches the manure guy work, a huge shadow covers the whole place. An instant cut later, it's all sunny, revealing it was shot at a different time of day.
Continuity mistake: After Marty gets to 1885, a bunch of Indians are running to him and the cavalry behind them, but in the open view one second before, the cavalry was not there.
Continuity mistake: In 1955 while the Doc is recording some stuff, while Marty behind him is sleeping on the couch, his head moves from side to side between shots.
Continuity mistake: When Doc realises that his name has disappeared from the tombstone, the date on the tombstone remains, but in the next shot, it disappears. (01:07:47)
Continuity mistake: When Marty is about to race against needles, the camera zooms in towards his car. Notice a big rectangular black object reflected on the car. From opposite angles it disappears and there's just green fields. The black object was most surely a structure to hide the camera equipment.
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