Continuity mistake: When Doc's about to send Marty back to 1885 from 1955, and Marty's dressed up...when Doc's walking back and forth loading up the car - look at the shadow from the building. You see it changes by several feet in a few seconds as the scene was obviously shot throughout the day. (00:16:35)
Factual error: When the red Presto-log is burning, rivets begin to blow out of the locomotive, supposedly from the pressure. The rivets in the boiler, which would be subjected to pressure, are not visible on the outside of a locomotive. The rivets which are seen to blow out in the movie are in the smokebox, an area which is subjected to heat and smoke, but no steam pressure. (01:40:10)
Plot hole: Although Marty rips the fuel line, not all the fuel would have drained out of the tank. Only the fuel that was already in the fuel line would have leaked out, meaning it could simply be patched, bled and the engine would run without a problem.
Factual error: In 1885, Hill Valley and its surrounding areas are shown as having a desert climate, when in both 1955 and 1985, the climate is grassland. In reality, Nevada County, California (where Hill Valley is supposed to be located) is and always has been grassland and forests, not arid desert.
Other mistake: When the movie ends and Doc says, "It means your future hasn't been written yet," watch his son Verne behind. He stares at the camera, calls someone from the crew, waving his hand, and points at his crotch. Seemingly, the kid was having a hard time trying not to pee on himself.
Factual error: Each time one of the special Presto-logs begins to burn the locomotive suddenly accelerates. In real life the logs would heat the water faster and generate more steam, but there would be an appreciable time-lag between the time the logs begin to burn and the engine accelerates. Also, train engines must accelerate slowly. If too much power is applied the drive wheels merely spin on the rails. (01:35:20)
Revealing mistake: At the very end of this film, Doc appears in his locomotive time machine. In every shot the plate which says 'ELB' changes color. From red to orange. You would say this is a change in light angle, but when the locomotive rises and turns, you can see every angle of this plate and in every angle this plate is red. (01:48:55)
Revealing mistake: In the overhead shot of the train explosion, you can tell which explosion is 'real' and which one is fake - the second explosion appears out of nowhere from the first one. (01:42:00)
Continuity mistake: When Marty is inside the cave (where he hides the DeLorean), keep a close eye on the huge landscape and very large mountains behind Marty when he is screaming at the bear. The entire background changes when he runs out of the cave to just a few hundred yards of ground before it drops down, where Marty falls into the fence. What happened to the vast landscape and mountains? (00:20:30)
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.