Other mistake: In Sarah's room, after the close-ups of Lancelot's empty shelf space and of Sarah beginning to say, "Someone..." as she finishes, "has been in my room again," in this wide shot, while still on her bed until she leaves her room, there is a mark across Sarah's forehead that extends to the left side of her eye. It isn't in the previous or following shots. (00:06:40)
Other mistake: When Sarah is in the room with the old hag who lives at the rubbish dump, the old hag asks, "What's the matter, dearie? Don't you like your toys?" Connelly is mouthing the hag's lines, presumably as a prompt to recall her own lines. (01:10:45)
Other mistake: When Sarah is at the end doing her speech with David Bowie in that upside down world and is meant to recite the speech word for word, she forgets the line "To take back the child that you have stolen" Instead she skips right over the line and says, " I have fought my way here to the castle beyond the goblin city - - missed line - - for my will is as strong as yours...etc. Etc."
Other mistake: As the cannon the Goblin army brings rolls to a stop, the smoke jet used to simulate shots is visible.
Other mistake: As Sarah looks at the opening that she can't readily see, the vine on the right side goes from sharp to blurry at the top of it.
Answer: The necklace is a symbol of Jareth's power throughout the story. All the time that Sarah is in the Labyrinth, Jareth has more power than her, because she doesn't really know what she's doing, and isn't taking one particular path, just getting lucky at the right times. At the end, as we all know, Sarah triumphs, and Jareth's necklace changes to admit his defeat.