Revealing mistake: There's one bit where we see the shark slamming into a boat and gliding along the side with its mouth open. Not only does the shark's latex mouth bend beneath the snout, narrowing from pressure, but within the mouth you can clearly see yellow hydraulic tanks to open the mouth. (01:22:05)
Visible crew/equipment: Near the beginning when Lois and Clark are walking out of the Daily Planet, Clark gets stuck in the revolving doors. But, look closely at the glass door, and you can see Richard Donner (confirmed in Superman expanded commentary) holding the door so that Christopher Reeve can get stuck.
Revealing mistake: During the final chase between the son of the Sheik and the evil oil company henchman, Tomas Milian is replaced on the speedboat by a stuntman wearing a bad wig in some shots, and in other shots by the cutest little puppet that rides the cutest little toy boat. (01:23:00)
Revealing mistake: After the birthday dinner and dance, the exterior shots of snow falling show the snow being sprayed from a lower point on the right side of the screen. Shot changes and now it's being sprayed from somewhere behind the bleachers.