Right before Ted chugs the beer, his shirt is buttoned up all the way. In the next shot, it is partially unbuttoned.
When Marty is talking to Caroline while he gets undressed, he just takes off his shirt. He clearly has his jeans on in that entire part. He then rips open the curtains and still has his jeans on, yet in the next cut, in which the camera is in front of him, he is completely naked, no clothes whatsoever.
When Marty comes out of the locker room after throwing up, the tissues he is holding switch from his left hand to his right hand and back.
When Shirley is burned in the acid bath, her position and facial burns change between shots. First she drowns unconscious from the burns, and has obvious marks on her face from the acid. The next two shots, the others hear her screaming, and then she's struggling to pull herself out of the tub, but her facial burns have disappeared. Next shot, she's suddenly still again; her face, now changed to a waxy state which breaks off like cement; just as the others arrive to find her. Realistically her face should be melting away or peeling off. Next shot, the surviving group enter the bathroom to find the shriveled remains of a skeleton.
Some believe that the letterman jacket worn by Marty disappears as he is splashed with acid. However, Marty is NOT wearing the jacket, but it is resting over his shoulders (notice it shake when he moves). As he is trying to turn off the gas after the fire begins, you can see the jacket start to slide down his back. When he is on the ground, you can see he is laying on it.
In each sequential or consecutive opening scene involving Marty inside the school lab, it is way obvious that the camera is jostling the shelf containing the nitrite acid. Two times, he is standing away from the shelf, so he cannot possibly bump it. And another time, he is putting the bottle back in its spot, after pouring some into a beaker. However such maneuver would not cause the shelf to simply wiggle or move. And no chemical lab would have a flimsily constructed shelf, holding very dangerous or toxic chemicals.
When the bullies are manhandling Marty and dunking him in the toilet at the beginning, Marty has been replaced by a very obvious mannequin.
It's quite obvious that all (or almost all) of the actors playing high-school students at the start of the film are quite beyond the age.
When Ted finds his old shoes in his locker, he hands them to Skip and says "There you go, Skip. You're always borrowing from me anyway." But his mouth doesn't move.
When the guests arrive at the school for the reunion, they are all surprised that it is closed up and abandoned. However, several of the guests still live in the town, so they would have known that the school had closed down.
The students are supposedly attending their 10-year reunion, which would mean they graduated in 1976, yet there is a reference that they're the Class of 1980.