Revealing mistake: When Doc and Marty arrive in 2015 when the car is landing in the alley you can see the mechanism that is lowering the car. Just as the scene switches from the front of the car (right after the headlights go out) to the back of the car, look between the car and the building at the same level as the back bumper. There is something that is moving down with the car. Also, the vents in the back of the DeLorean are different.
Revealing mistake: When Marty, in the 1955 dance, looks at his father with his binoculars, you can see that the angle of the binoculars are really misplaced. Marty is looking at him at his far front, but the binoculars' image comes more from the floor. In fact, what the binoculars show is from the first film.
Revealing mistake: When Griff and his gang are flying through the air and about to crash into the courthouse after the hover board chase, look at the girl on the left. Her legs hit one of the building's pillars, and her body rotates sideways, but she continues moving forward - obviously suspended by wires.
Revealing mistake: When Marty is burning the almanac, during the lightening strike, the shadow of the post holding the hover-board off the ground is visible. - watch the hoverboard when the scene is illuminated by lightning strikes. The post holding up the hoverboard is also clearly visible when they pan around Marty as he is holding the burned rope from the Delorean.
Revealing mistake: When Biff and his gang are chasing Marty on the hoverboards in a few shots after Marty is hanging off the back of the Jeep, when the shot shows the gang catching up, the Jeep goes through some wet places in the street, showing the camera car's tire tracks. They're not the Jeep's because the tire tracks are double-wheeled and the Jeep was not turning in that shot.
Revealing mistake: Throughout this movie and Part III, whenever there is a special effect, like two Biffs in one scene, the scenes with the flying cars, and basically whenever an actor is playing three or four roles at the same time, if you look very carefully, you can see the picture flash ever so slightly repeatedly. It looks almost as if the picture is throbbing a bit. Might be more visible if viewed on the DVD.