Continuity mistake: When the statue of Liberty is about to crash on the street, a close shot is seen of jammed cars and hysterical people. When the shot changes to Superman flying to the rescue, the jam, the cops and the people have disappeared, and all is nice and quiet in Metropolis.
Revealing mistake: In the scene where they're tumbling down the hill, Buttercup has a beard.
Continuity mistake: After trying to entice the primitive tribe with flashy clothes and a boom box, Alvin and Simon get tied to a hut. The four ropes around their wrists are initially tied together in one knot right above their heads. But once they notice that Theodore is being pampered like a god, Alvin and Simon's wrist ropes are suddenly knotted separately instead. (00:51:05)
Visible crew/equipment: When the blob just misses Laverne, you can see a crew member under the raft (probably operating the mechanical special effect).
Other mistake: When He-Man is fighting against the centurions on the floating disks, he tells the others to get inside a building. As he opens the door to the building, not only does it fall right off the hinges, but his sword also falls right off his back, pulling his cape off with it just as the scene ends. (01:09:20)