Deliberate mistake: At the end fight scene, when they are in the barn one of the men falls crashes through the wall when they get hit, spilling the fight to the outside. Unless the barn's walls were made of cheap plywood, the wall would not have given away so easily. Obviously done for dramatic purposes.
Deliberate mistake: In a couple of scenes, Bandit's Trans Am's engine sounds are dubbed, and you can hear the shifting of a manual transmission when his car was an automatic.
Deliberate mistake: When the villains rampage the White House, the flag's base remains on the ceiling, and the flag pole falls inside the house. So the final scene with Superman carrying the flag and its base as if it had been previously stolen or destroyed, is nonsensical, but it looks very patriotic indeed.