Revealing mistake: Fred is reading from "The Joanna Rhodes Beauty Book" and the title is shown on the dust cover. When Fred tilts the book, though, the words "Winston S. Churchill" are visible on the actual book under the dust cover. Also visible is the script from which the actor is reading, tucked inside the book and held by clips.
Audio problem: During the dream sequence, while the spirits of Christmas uses echoing sounds in their voices periodically, Fred's voice was not supposed to echo at all, but his voice can be heard echoing as well a few times.
Visible crew/equipment: As Bruinhilda starts to come out to do her number, the shadow of the boom mic is on the wall.
Factual error: During the meeting with American prisoners the lone woman says she's fought in both the European and Pacific theaters. Unless I'm mistaken, nobody got shipped from one to another during the war unless one theater was done.
