Revealing mistake: When Bluto is watching the sorority girls have their pillow fight and he falls down with the ladder, you can see him land on a grass mat that is cut into the lawn. It's funny because you can see the grass push in. (00:40:00)
Visible crew/equipment: In the scene during the American bandstand, at the end of the song when the teacher is dancing in front of the band members, the crews can be seen. The dressing and the hair doesn't match Grease era at all, and someone is sitting on a director's chair as well. (01:06:20)
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)
Continuity mistake: During the first meeting between Lou and Madeline Kahn, her fur stole changes position between shots almost more often than she changes names. (00:09:30 - 00:10:30)
Visible crew/equipment: Near the start, after the chopper crashes in the field, while Jack Riley is talking to Von Schauer and George Wilson we can see the small microphone clipped to Jack's shirt under his tie. (00:05:40)