Continuity mistake: When one of the stormtroopers unties Han Solo before he is put into the carbonite, watch his wardrobe - he has a disappearing / reappearing jacket on. This is fixed to an extent on the DVD - the jacket is now lightened to almost match his shirt, but it's still shiny like leather. (01:32:05)
Suggested correction: It just looks like a jacket because it's a shadow.
Continuity mistake: There are a couple of instances in the movie where the models do not correspond with the actual sets. When Klytus arrives at the Hawkmen city he lands near the top of the city. Yet in that very hall there is a pit with a deep void underneath. Such a room could only exist at the bottom of the city. Also, when the Hawkmen start to land on Ajax, its engine section appears to be missing. (01:10:10 - 01:14:30)
Revealing mistake: Right after one of the Mountie's cars is split in half by the snowplow, you can see the mini-wheel used to keep the half-car propped up.
Continuity mistake: Just before the Mystery Girl blows up the building in which Elwood resides, a police car with lights on its roof pulls up outside. When the building actually explodes just over a minute later, you see that the police car parked outside no longer has any lights. (00:39:54)
Visible crew/equipment: When Superman is fighting Non under the New York Streets (in the sewers), manhole covers start to jet up in the sky. When the first manhole cover shoots up you can quite clearly see the gas tube in the hole and the gas cylinder attached to the cover.