Continuity mistake: After the truck falls off the bridge, before Superman arrives a red truck passes by a green one and keeps on to the other end of the bridge. When the angle changes, a split second later, the red truck is now several feet back, not running and parked next to the green truck.
Revealing mistake: When the two Supermen are fighting in the scrapyard: As evil Superman comes flying out of the acid with his hands cupped, look at his cape. It is wrapped around the front of his waist and legs, not flapping backwards like it would be if Supes was flying forward at speed. Evil Superman is also completely dry during this shot (NOTE: Superpowers have nothing to do with this). This reveals the fact that it was shot with Christopher Reeve (or the stuntman) falling backwards into the vat, then shown in reverse.
Continuity mistake: When the bus that Clark and Jimmy are on pulls up to the traffic jam, you can see the smoke from the fire is wafting all over the place. When the angle changes when the two climb off the bus, however, the smoke is limited to the distant view.
Factual error: When Richard Pryor is working his job in the computer room his boss walks up behind him and is amazed at a program that Pryor has written. The boss asks how he did it; Pryor answers that even he doesn't know. Look at the computer screen - Pryor's amazing computer program is just a bunch of worthless print commands that print sentences onto the computer screen; it serves no real function whatsoever.
Other mistake: The movies show that Superman can talk and live in space as normally as on earth, with no extra effort needed. Therefore, the scene of Superman choking and suffering inside a shield/ bubble with no air is totally senseless. The Krypotnite laser which does choke him appears after he has destroyed the bubble.