Deliberate mistake: When Jamie Lee is picked up hitch hiking, the view out the front windshield, while pulling over to pick her up, is identical when they pull over moments later after all the windows are shattering.
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.