Deliberate mistake: When Old Biff and Young Biff are sitting in Biff's car, the car's rear-view mirror vanishes during all shots of Old and Young Biffs together. Presumably this made the split-screen effect easier to do.
Directed by: Robert Zemeckis
Starring: Christopher Lloyd, Michael J. Fox, Lea Thompson, Thomas F. Wilson, Elizabeth Shue
Deliberate mistake: When Old Biff and Young Biff are sitting in Biff's car, the car's rear-view mirror vanishes during all shots of Old and Young Biffs together. Presumably this made the split-screen effect easier to do.

Revealing mistake: In the scene where Doc Brown is following Biff into the tunnel, as Marty starts to pass between the cars on his hoverboard, one of the wheels on the rig supporting the hovering DeLorean is visible. (01:30:30)
Biff: Go ahead, kid. Jump. A suicide will be nice and neat.
Marty: What if I don't?
Biff: [raising gun] Lead poisoning.
Marty: What about the police, Biff? They're gonna match up the bullet with that gun.
Biff: Kid, I own the police. Besides, they couldn't match up the bullet that killed your old man.
Marty: You son of a...
[Biff pulls back on the gun's hammer.]
Biff: Suppose it's poetic justice. Two McFlys with the same gun.
Answer: At the end of the first film, Doc says, "what the hell" in response to the letter Marty gave him. So this shows it is not that strong a conviction, especially in the face of definite knowledge about something bad happening. It is also a way for Doc to repay Marty.
MasterOfAll