Revealing mistake: When the hovering object walking the dog in 2015 flies by, a moment before it disappears, you can see the wire used to support it.

Revealing mistake: As Doc drops Marty off behind Biff's car, the camera pans across the DeLorean, and we can see Christopher Lloyd has been replaced by a stunt driver. The stuntman can be seen trying to obscure his face. (01:30:26)
Revealing mistake: When the movie begins and the car takes off (achieved with a scale model car) note Doc's stiffness and fuzzy hair, revealing he was replaced by a dummy.
Revealing mistake: Doc and Marty hide in the alleyway while the flying police car takes 1985-Jen home. Problem is, Doc stares in awe at the sky before the police car is in view.

Revealing mistake: When Doc flies the DeLorean up and the wheels get stuck to a banner string, the close-ups of Doc show a lit cockpit, but the shots from the outside show it's dark and one can't really see who's at the wheel. However, for a couple of seconds you get to see it's not Doc but a stunt double or a stiff dummy. (01:23:25)

Revealing mistake: When Doc holds the newspaper with the 'Gang jailed' headline, the same paragraph is repeated several times. (00:24:03)
Answer: Yep, and there is, but they're both elsewhere. Doc's been committed to an asylum somewhere. When Marty first meets the alternate Biff, Biff tells him that he's supposed to be in Switzerland at boarding school - that's where the alternate Marty is.
Tailkinker ★
Wouldn't someone probably see Doc and report that he escaped from the asylum?
Maybe, but no way to be sure, and they're not around long enough for that to be an issue anyway.
Jon Sandys ★