Elphaba is not wearing the bag containing the Grimmerie when she leaves the Emerald City on her broom.
During 'What Is This Feeling?', while the screen is split, Elphaba looks to her left and uses her right arm to grab her covers in order to throw them off. But in the next shot she's facing her right and using her left arm to throw off the covers which is the correct direction for the room.
During "Dear Old Shiz", shortly before Galinda starts singing, there is a close up of the back of Elphaba's head. As can be seen in the background of that shot, everyone makes way for her, leaving only Galinda who didn't notice Elphaba yet. Yet, when Galinda sings and the camera switches to a perspective in front of her, there are still people behind her and they only move simultaneously with Galinda recoiling.
When the black hat is first introduced, its brim is frumpier than can be seen in the mirror shots of Pfannee holding the hat. The brim appears slicker in the mirror, more akin to how it appears when Elphaba wears it. This indicates the hat didn't look ugly enough in their first take, and the take had to be redone with the brim furled up for their distaste to make more sense.
At the beginning, when the Scarecrow, Dorothy, the Tin Man, the Lion, and Toto walk from Elphaba's castle towards the Emerald City (after having melted the witch), Dorothy carries the Witch's broom with all its bristles. But in Le Magicien d'Oz (1939), the Witch burns the bristles of her broom to burn Scarecrow, and when they present the broom to the Wizard, the bristles are burned off. Also, as evidenced by Nessarose being given silver shoes, rather than ruby slippers, the film isn't a prequel to the 1939 film, but rather its own continuity. It's more than likely that the state of Elphaba's broom will be consistent with the upcoming "Wicked: For Good".
During "No One Mourns the Wicked", there was no evidence of the Kansas farmhouse that had recently fallen from the sky and crushed Nessarose.
However, "No One Mourns the Wicked" is a song celebrating the death of Elphaba, the wicked witch of the west, not her sister's. Her sister's death happened quite a while before that, enough time that the munchkins probably had her and the house that crushed her removed from the village, since Dorothy's entire adventure takes place between Nessa's death and Elphaba's.
Elphaba loses control of her powers whenever she gets angry. Yet, when Galinda teases her with her mother's bottle and she yells at her, nothing happens. Though, given that Elphaba is not in her strongest emotion at this point, not to mention having no such build-up pressure to it either, her magic doesn't respond as a result.
In the classroom scene where Elphaba causes the poppies to rise in the air and the pollen sends the students to sleep, we can clearly see a wire suspending one of the flowers as it moves.
When the balloon arrives with Elphaba's invitation to visit the Wizard, a blur can be seen moving across the steps in the background. This is caused by the post-production removal of the wire supporting the balloon.
Fiyero is supposed to have blue eyes. For some scenes however, we can see that Jonathan Bailey does not wear the colored contacts and his eyes are brown, his natural eye color.
Right after "Dear Old Shiz", the scene where Galinda tells Elphaba the iconic line "You're green!" in one of the parts where it is a close up of Cynthia Erivo (Elphaba), we can clearly see she is wearing a wig.
In the movie the two letter abbreviation for Nebraska, NE is used. Two letter state abbreviations weren't introduced until 1963. The Wizard appears to be a man of the late 19th and early 20th centuries. The correct abbreviation for the time would likely have been Nebr.