When the Junk lady gives Sarah the statue of the princess in her room, stating that it's not junk, she hobbles over to her, but when it switches back to face the Junk lady, she's back in her original spot and the statue is still on the table.
Jennifer Connelly's weight changes drastically throughout the course of the film. Comparing the ballroom sequence with the meeting of Hoggle (pond) her face is considerably plumper (cheeks). Also this is sometimes visible during scenes.
When Jareth transforms from the beggar to himself he throws his costume behind himself to the left several moments later he again has the costume in his hands and he throws it behind himself to the right.
In Jareth's first song, he holds Toby, throws him upwards and leaves him for a goblin to catch. When Toby is in Jareth's hands he is with his face towards the camera. When in the air he turns around before being caught by the goblin - but his face remains towards the camera.
In the scene where Sarah is with the JunkWoman in her pretend room, the Junkwoman hands her her lipstick and tells her to make herself up with it. In the next shot we see Sarah with perfect red lipstick on, yet there didn't appear to be time for her to apply it.
Sarah throws stones to distract the Goblin corps from Ludo. She is hiding behind a hedge. When she picks the second stone, she steps back behind the hedge, but after a cut she stands in front of it and throws the stone.
In the Escher-style sequence at the end, when Jareth goes from underneath the walkway that Sarah is on, and turns up onto the top of the walkway, the hydraulic rod that propels him up there can visibly be seen in the shadow that is cast on the wall behind him.
During the battle in town, the summoned rocks that are supposed to roll from the left to right of the screen, has at least one rock that isn't rolling at all, showing it's being dragged by an unseen wire or rope of some sort.