In the scene where He-Man is running from the Air Centurions, when he goes in the door to the warehouse, his sword and cape fall off his back. In the next frame, when he is running up the stairs everything is in place again.
During the climactic battle scene at Castle Grayskull, He-Man jumps up onto a high platform and starts running. There is a bad edit, and it cuts to He-Man running before his feet land. There is also no sound of his feet hitting the platform.
Throughout the movie, particularly in the beginning with one of the first fight scenes, He-Man appears to have a gash on his upper chest/shoulder area. It switches from right to left and back again several times.
When He-Man hangs upside down while pursued by Skeletor's Air Centurion, his hair does not hang down. However, since he's "hanging from" an anti-gravity platform, on which he's standing, from his point of view he's standing the right side up. If his hair would fall down (the real down), then his entire body would follow, but that does not happen. Apparently, that's how those anti-gravity platforms work.
The keyboard that Kevin got from the music store seems to play back to front, with the high notes to the left.
The keyboard is seen as it would appear from Teela's point of view, therefore the high to low range of the notes is still correct.
When Karg leads Skeletor's troops charge into Gwildor's home, he tells his men to "find the key". It is impossible for him to have known about a second cosmic key as his superiors did not even know until shortly later on.
When Gwildor asks Kevin and Julie if there's any point in time they wish to go, Kevin says to just send them both home. As Julie and Kevin go through the portal that Gwildor opened, Julie quickly turns around and tells Gwildor to send them back. Before she can say anything else, Kevin drags her into the portal. Julie then wakes up in her bed and finds she had been taken back to the day her parents died. There's no way Gwildor should have been able to do it since he knows nothing of the death of Julies parents or when they died.
Near the end of the movie, Detective Lubic pumps the slide on his shotgun three times before firing another shot. He does this as a) a threat, b) a fear-response and c) determination to act, but he is either emptying the gun or, as no shells come out, is using an empty weapon which, surprisingly, actually shoots when he gets around to pulling the trigger.
During the final battle in Castle Grayskull, He-Man is hiding behind one of the huge stone pillars with a laser gun he took from a trooper. He makes the motion of firing the gun three times, but only two laser shots come out.
Before He-Man surrenders himself to Skeletor on the roof top, a group of troopers try to subdue him by pinning him down. As they are doing so another trooper runs towards them, trips over a body on the floor and appears to fall into He-Man.
When He-Man's friends use the Cosmic Key to return to Castle Grayskull, when He-Man is seen in close-up, the shackle on his left wrist is missing. Before and after the close-up, He-Man's wrists are shackled and chained to the throne room floor.
Gwildor mentions to Julie that the Cosmic Key can take her to the past or the future which he proves by actually sending Julie back in time before her parents are killed. It is also shown that Julie merges with her past self and it not a duplicate observer of the past. If the Cosmic Key is able to manipulate time in this fashion, then why didn't he use it with He-Man, Duncan, and Teela at the beginning to send them back in time to prevent Skeletor from stealing the Cosmic Key? Gwildor could have used the Cosmic Key to send them back in time to before Gwildor invented the key and stopped himself from inventing it, much the same way Julie stopped her parents from getting on the plane.