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.
Back to the Future Part II (1989)
1 deliberate mistake - chronological order
Directed by: Robert Zemeckis
Starring: Christopher Lloyd, Michael J. Fox, Lea Thompson, Thomas F. Wilson, Elizabeth Shue
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: Oh! Nice dress, Lorraine. Although, I think you'd look better wearing nothing at all.
Lorraine: Biff, why don't you take a long walk off a short pier?
Biff: Hey listen, Lorraine. Now that I got my car all fixed up I figured I cut you a break and give you the honor of going with the best looking guy in school.
Lorraine: Yeah, well, I'm busy.
Biff: Oh, yeah? Doing what?
Lorraine: Washing my hair.
Biff: Oh, that's about as funny as a screen door on a battleship.
Marty: Screen door on a submarine, you dork.
Trivia: When Doc and Marty arrive back in 1955 to stop the handover of the Almanac, there are 4 versions of the time machine in the area at that time - the one they just arrived in from the alternate 1985, the one Marty arrived in from the original 1985 in the first film, the one Biff arrived in from 2015 in the second film, and the one Doc buried in 1885 in the third film.
Answer: He is attempting to play the song "The Power Of Love" by Huey Lewis and The News. He was first seen playing it very well in the first Back To The Future movie when he was trying out for the school dance. Jennifer recognizes the song and is shocked that Marty who was so good at guitar was suddenly able to hardly play it.