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)
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. (00:06:12)
Revealing mistake: When Biff cocks his revolver in the alternate 1985, you notice that the chambers rotate in the wrong direction. This is either a flipped shot or a mistake caused by the prop gun.
Revealing mistake: As Doc and Marty go to the soon-to-be Lyon Estates in 1955, the DeLorean hovers over the camera. Look at the roof. You can see 3-4 wires attached to the time machine.
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 Marty goes to burn the almanac he flips the hover-board to his hand. The board begins to flip up before Marty touches it and even so, he doesn't touch it at all, he steps his foot behind it. (01:35:19)
Revealing mistake: When the DeLorean is flying behind Biff's car, you can see the wheels of the DeLorean rolling along the ground. This is evident when the car turns to fly away after Marty is deposited on the back of Biff's car. (01:30:28)
Revealing mistake: When the Doc of the future is in 1955 and sees the DeLorean, his hair is short (in fact you can see that the actor is wearing the wig that he wore for the 1955 Doc), but after a shot to Marty and back again, his hair is the same length as it was in 1985.
Revealing mistake: When old Biff and young Biff are discussing the Sports Almanac in young Biff's car in the garage, young Biff tosses the Almanac into the air, landing in the back seat next to Marty. When it's thrown in the air his hand and the Almanac become transparent.
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 Doc and Marty are driving on the Sky Way Doc says "damn this traffic," but in the reflection of the DeLorean's front window there are no cars.
Revealing mistake: After Old Biff steals the DeLorean, he backs it up into a dumpster and several trash bags. The dumpster and the bags move before the DeLorean touches them. (00:32:50)
Revealing mistake: During the hoverboard chase in 2015 between Griff and his gang and Marty, you can plainly see the wires holding the gang up on their hoverboards in the wide shots as well as on the Jeep Wrangler before it lands in front of Marty.
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 Marty and Strickland are talking in the Alternate 1985, pay attention to Strickland. Every time Marty is talking, you see Strickland moving his cheeks. He is mouthing Marty's lines.
Revealing mistake: When Griff 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: During the tunnel chase at the end of the movie, in the shot shown from the ceiling of the tunnel, you can see in the shadow of the hover-board, skate-board wheels.
Revealing mistake: When Biff steals the DeLorean and flies off with it, the DeLorean disappears just before it reaches the top of the screen. It appears to just wipe out of frame before it's supposed to. This mistake is visible on the Netflix version.
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: 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.
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.
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.